{"id":11494,"date":"2021-05-22T19:52:47","date_gmt":"2021-05-22T14:22:47","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/ol\/?p=11494"},"modified":"2021-05-26T12:58:40","modified_gmt":"2021-05-26T07:28:40","slug":"equations","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/ol\/ordinary-level\/equations\/","title":{"rendered":"\u0db4\u0dcf\u0da9\u0db8\u0dca \u0d85\u0d82\u0d9a\u0dba &#8211; \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?id=1Xfd74wulLDsyEulFDtQfKsXzLBEPrVG4&amp;export=download\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u0dc0\u0dd3\u0da2\u0dd3\u0dba \u0db7\u0dcf\u0d9c \u0dc3\u0dc4\u0dd2\u0dad \u0d92\u0d9a\u0da2 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"386\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-17.png\" alt=\"\" class=\"wp-image-11495\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-17.png 358w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-17-278x300.png 278w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-17-150x162.png 150w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-17-300x323.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u0dc3\u0db8\u0d9c\u0dcf\u0db8\u0dd3 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"288\" height=\"546\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-18.png\" alt=\"\" class=\"wp-image-11496\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-18.png 288w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-18-158x300.png 158w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-18-150x284.png 150w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-18-222x420.png 222w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u0db7\u0dcf\u0d9c \u0dc3\u0d82\u0d9c\u0dd4\u0dab\u0d9a \u0dc3\u0dc4\u0dd2\u0dad \u0dc3\u0db8\u0d9c\u0dcf\u0db8\u0dd3 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab<\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"430\" height=\"445\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19.png\" alt=\"\" class=\"wp-image-11497\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19.png 430w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19-290x300.png 290w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19-150x155.png 150w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19-300x310.png 300w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-19-406x420.png 406w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"651\" height=\"192\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-20.png\" alt=\"\" class=\"wp-image-11498\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-20.png 651w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-20-300x88.png 300w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-20-150x44.png 150w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"text-decoration: underline\">\u0dc3\u0dcf\u0db0\u0d9a \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8<\/span><\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"203\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-21.png\" alt=\"\" class=\"wp-image-11499\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-21.png 297w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-21-150x103.png 150w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-21-218x150.png 218w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"text-decoration: underline\">\u0dc0\u0dbb\u0dca\u0d9c \u0db4\u0dd6\u0dbb\u0dca\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8<\/span><\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"497\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-23.png\" alt=\"\" class=\"wp-image-11501\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-23.png 297w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-23-179x300.png 179w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-23-150x251.png 150w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-23-251x420.png 251w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">\u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8<\/h4>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"401\" height=\"108\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-24.png\" alt=\"\" class=\"wp-image-11502\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-24.png 401w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-24-300x81.png 300w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-24-150x40.png 150w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/figure><\/div>\n\n\n\n<p>(1)<\/p>\n\n\n\n<p>a.\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac x{(x-1)}+\\frac{3x}{2(x-1)}=\\frac54<\/span>\n\n\n\n<p>b.\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba\u0da7 \u0d89\u0da9\u0db8\u0d9a \u0d8d\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dd9\u0dc4\u0dd2 \u0d9a\u0db8\u0dca\u0db6\u0dd2 \u0dc0\u0dd0\u0da7\u0d9a\u0dca \u0db6\u0dd0\u0db3 \u0dc0\u0dd9\u0db1\u0dca\u0d9a\u0dbb \u0d87\u0dad.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"93\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-25.png\" alt=\"\" class=\"wp-image-11504\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-25.png 246w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-25-150x57.png 150w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><\/figure><\/div>\n\n\n\n<p>I.\u0db8\u0dd4\u0dc5\u0dd4 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba 30cm<sup>2 <\/sup>&nbsp;\u0db1\u0db8\u0dca 2x<sup>2<\/sup>+ x = 10 \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1<\/p>\n\n\n\n<p>II.\u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc0\u0dd2\u0dc3\u0db3\u0dcf x \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>III.\u0dc3\u0db8\u0dca\u0db4\u0dd6\u0dbb\u0dca\u0dab \u0d89\u0da9\u0db8\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>(2)<\/p>\n\n\n\n<p>a).\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>b)<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\;\\frac3x+\\frac2y=\\frac58<\/span><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\;\\frac2x+\\frac1y=\\frac18<\/span><\/p>\n\n\n\n<p>c).\u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd \u0daf\u0ddc\u0da9\u0db8\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd \u0db8\u0dd9\u0db1\u0dca 4 \u0d9c\u0dd4\u0dab\u0dba\u0d9a\u0da7 \u0dc0\u0da9\u0dcf \u0dbb\u0dd4\u0db4\u0dd2\u0dba\u0dbd\u0dca \u0daf\u0dd9\u0d9a\u0d9a\u0dd2\u0db1\u0dca \u0dc0\u0dd0\u0da9\u0dd2\u0dba. \u0daf\u0ddc\u0da9\u0db8\u0dca \u0d9c\u0dd9\u0da9\u0dd2 \u0dad\u0dd4\u0db1\u0d9a\u0dca \u0dc4\u0dcf \u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2 \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0d9c\u0dad\u0dca \u0dc0\u0dd2\u0da7 \u0db8\u0dd2\u0dbd 114 \u0d9a\u0dd2. \u0daf\u0ddc\u0da9\u0db8\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd x \u0dbd\u0dd9\u0dc3 \u0d9c\u0dd9\u0db1<\/p>\n\n\n\n<p>I.\u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd x \u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1<\/p>\n\n\n\n<p>II.x \u0dc4\u0dd2 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0d9a\u0dca \u0d9c\u0ddc\u0da9\u0db1\u0d9f\u0dcf \u0d91\u0dba \u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>III.\u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1<\/p>\n\n\n\n<p>(3) 2017 \u0dc3\u0dcf.\u0db4\u0dd9\u0dc5 \u0d8b\u0db4\u0d9a\u0dcf\u0dbb\u0d9a \u0dc3\u0db8\u0dca\u0db8\u0db1\u0dca\u0dad\u0dca\u200d\u0dbb\u0dab\u0dba &#8211; \u0d9c\u0dab\u0dd2\u0dad\u0dba II)<\/p>\n\n\n\n<p>\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1\u0dca\u0db1\u0dda PQR \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dd2 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dcf\u0d9a\u0dcf\u0dbb \u0dbd\u0dd1\u0dbd\u0dd2 \u0d9a\u0dd0\u0db6\u0dd0\u0dbd\u0dca\u0dbd\u0d9a\u0dd2. \u0d91\u0dc4\u0dd2 PST \u0dc3\u0dd8\u0da2\u0dd4 \u0d9a\u0ddd\u0dab\u0dd3 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3 \u0d9a\u0db4\u0dcf \u0d89\u0dc0\u0dad\u0dca \u0d9a\u0dbb\u0dba\u0dd2. SP \u0daf\u0dd2\u0d9c \u0d92\u0d9a\u0d9a a \u0dc0\u0dda. ST \u0daf\u0dd2\u0d9c SP \u0daf\u0dd2\u0d9c\u0da7 \u0dc0\u0da9\u0dcf \u0d92\u0d9a\u0d9a \u0dad\u0dd4\u0db1\u0d9a\u0dca \u0dc0\u0dd0\u0da9\u0dd2\u0dba. SQ \u0daf\u0dd2\u0d9c SP \u0daf\u0dd2\u0d9c \u0db8\u0dd9\u0db1\u0dca \u0daf\u0dd9\u0d9c\u0dd4\u0dab\u0dba\u0d9a\u0dd2. QR \u0daf\u0dd2\u0d9c \u0d92\u0d9a\u0d9a 3a+9 \u0dc0\u0dda. \u0d9a\u0db4\u0dcf \u0d89\u0dc0\u0dad\u0dca \u0d9a\u0dc5 \u0d9a\u0ddc\u0da7\u0dc3 \u0dc4\u0dd0\u0dbb \u0d89\u0dad\u0dd2\u0dbb\u0dd2 \u0d9a\u0ddc\u0da7\u0dc3\u0dda <img loading=\"lazy\" decoding=\"async\" width=\"2\" height=\"15\" src=\"\">\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a 28\u0d9a\u0dd2. \u0dc0\u0dbb\u0dca\u0d9c\u0da2 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0d9a\u0dca \u0d9c\u0ddc\u0da9\u0db1\u0d9f\u0dcf \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0dd9\u0db1\u0dca SP = \u0d92\u0d9a\u0d9a<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{(\\sqrt{37}-3)}2<\/span>\u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0dcf \u0d9a\u0db4\u0dcf \u0d89\u0dc0\u0dad\u0dca \u0d9a\u0dc5 \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a 3 \u0d89\u0d9a\u0dca\u0db8\u0dc0\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"185\" height=\"152\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-26.png\" alt=\"\" class=\"wp-image-11511\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-26.png 185w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-26-150x123.png 150w\" sizes=\"(max-width: 185px) 100vw, 185px\" \/><\/figure><\/div>\n\n\n\n<p>(4)\u0d91\u0d9a\u0dca\u0dad\u0dbb\u0dcf \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0dcf\u0db8\u0dbb\u0dba\u0d9a \u0daf\u0dd2\u0d9c x+3 \u0dc4\u0dcf \u0db4\u0dc5\u0dbd y \u0dbd\u0dd9\u0dc3 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0d92\u0d9a\u0d9a 40 \u0d9a\u0dd2. \u0db4\u0dc3\u0dd4\u0dc0 \u0d9a\u0dcf\u0db8\u0dbb\u0dba\u0dda \u0db4\u0dc5\u0dbd \u0d91\u0dbd\u0dd9\u0dc3\u0db8 \u0dad\u0db6\u0dcf \u0daf\u0dd2\u0d9c \u0db4\u0dc3\u0dca \u0d9c\u0dd4\u0dab\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dc0\u0dd0\u0da9\u0dd2 \u0d9a\u0dc5 \u0dc0\u0dd2\u0da7 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0d92\u0d9a\u0d9a 104 \u0d9a\u0dd2.<\/p>\n\n\n\n<p>I.\u0d89\u0dc4\u0dad \u0dad\u0ddc\u0dbb\u0dad\u0dd4\u0dbb\u0dd4 \u0daf\u0d9a\u0dca\u0dc0\u0dd3\u0db8\u0da7 \u0dc3\u0db8\u0d9c\u0dcf\u0db8\u0dd3 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dba\u0dd4\u0d9c\u0dbd\u0dba\u0d9a\u0dca \u0d9c\u0ddc\u0da9\u0db1\u0d9c\u0db1\u0dca\u0db1<\/p>\n\n\n\n<p>II.\u0d91\u0dba \u0dc0\u0dd2\u0dc3\u0db3\u0dcf x \u0dc4\u0dcf y \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>III.\u0d9a\u0dcf\u0db8\u0dbb\u0dba\u0dda \u0db1\u0dc0 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>IV.\u0daf\u0dd2\u0d9c \u0d92\u0d9a\u0d9a 6 \u0dc4\u0dcf \u0db4\u0dc5\u0dbd \u0d92\u0d9a\u0d9a 5 \u0dc0\u0db1 \u0da7\u0dba\u0dd2\u0dbd\u0dca \u0d9a\u0dd0\u0da7 \u0d87\u0dad\u0dd2\u0dbb\u0dd3\u0db8\u0da7 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0db1\u0db8\u0dca \u0d92 \u0dc3\u0db3\u0dc4\u0dcf \u0da7\u0dba\u0dd2\u0dbd\u0dca \u0d9a\u0dd0\u0da7 \u0d9a\u0ddc\u0db4\u0db8\u0dab\u0d9a\u0dca \u0d8b\u0dc0\u0db8\u0db1\u0dcf \u0dc0\u0dda\u0daf?<\/p>\n\n\n\n<p>(5)(2015 \u0dc3\u0dcf.\u0db4\u0dd9\u0dc5 \u0d8b\u0db4\u0d9a\u0dcf\u0dbb\u0d9a \u0dc3\u0db8\u0dca\u0db8\u0db1\u0dca\u0dad\u0dca\u200d\u0dbb\u0dab\u0dba &#8211; \u0d9c\u0dab\u0dd2\u0dad\u0dba II)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"187\" height=\"127\" src=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-27.png\" alt=\"\" class=\"wp-image-11513\" srcset=\"https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-27.png 187w, https:\/\/learnsteer.sasnaka.org\/ol\/wp-content\/uploads\/sites\/2\/2021\/05\/image-27-150x102.png 150w\" sizes=\"(max-width: 187px) 100vw, 187px\" \/><\/figure>\n\n\n\n<p>\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1\u0dca\u0db1\u0dda \u0db4\u0dcf\u0daf\u0dba\u0d9a \u0daf\u0dd2\u0d9c (x+3) cm \u0dc0\u0db1 \u0dbb\u0ddc\u0db8\u0dca\u0db6\u0dc3\u0dba\u0d9a\u0dca \u0dc4\u0dd0\u0da9\u0dad\u0dd2 \u0d86\u0dc3\u0dca\u0dad\u0dbb\u0dba \u0d9a\u0dd2. D \u0dc3\u0dd2\u0da7 AB \u0da7 &nbsp;&nbsp;&nbsp;&nbsp;\u0dbd\u0db8\u0dca\u0db6 \u0daf\u0dd4\u0dbb (x-1) cm \u0dc0\u0dda<\/p>\n\n\n\n<p>I.\u0dbb\u0ddc\u0db8\u0dca\u0db6\u0dc3\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0db3\u0dc4\u0dcf x \u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0d9a\u0dca \u0dbd\u0db6\u0dcf\u0d9c\u0db1\u0dca\u0db1<\/p>\n\n\n\n<p>II.\u0dbb\u0ddc\u0db8\u0dca\u0db6\u0dc3\u0dba \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba 9cm<sup>2<\/sup> \u0db1\u0db8\u0dca x \u0db8\u0d9c\u0dd2\u0db1\u0dca <span class=\"wp-katex-eq\" data-display=\"false\">x^2+2x-12=0<\/span>&nbsp;\u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc3\u0db4\u0dd4\u0dbb\u0dcf\u0dbd\u0db1\u0dd4 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>III. \u0dc0\u0dbb\u0dca\u0d9c \u0db4\u0dd6\u0dbb\u0dca\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dc4\u0ddd \u0d85\u0db1\u0dca \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc0\u0dd2\u0dc3\u0db3\u0dcf \u0dbb\u0ddc\u0db8\u0dca\u0db6\u0dc3\u0dba\u0dda \u0db4\u0dd0\u0dad\u0dca\u0dad\u0d9a \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>(6) (2016 \u0dc3\u0dcf.\u0db4\u0dd9\u0dc5 \u0d8b\u0db4\u0d9a\u0dcf\u0dbb\u0d9a \u0dc3\u0db8\u0dca\u0db8\u0db1\u0dca\u0dad\u0dca\u200d\u0dbb\u0dab\u0dba &#8211; \u0d9c\u0dab\u0dd2\u0dad\u0dba II)<\/p>\n\n\n\n<p>\u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dd2 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0d9a\u0dbb\u0dca\u0dab\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0d91\u0dc4\u0dd2 \u0d9a\u0dd4\u0da9\u0dcf\u0db8 \u0db4\u0dcf\u0daf\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0db8\u0dd9\u0db1\u0dca \u0daf\u0dd9\u0d9c\u0dd4\u0dab\u0dba\u0d9a\u0da7 \u0dc0\u0da9\u0dcf 1cm \u0d9a\u0dd2\u0db1\u0dca \u0d85\u0da9\u0dd4\u0dc0\u0dda.<\/p>\n\n\n\n<p>I. \u0d9a\u0dd4\u0da9\u0dcf\u0db8 \u0db4\u0dcf\u0daf\u0dba\u0dda \u0daf\u0dd2\u0d9c <span class=\"wp-katex-eq\" data-display=\"false\">x\\;cm<\/span>&nbsp;\u0db1\u0db8\u0dca \u0d9a\u0dbb\u0dca\u0dab\u0dca\u0dba\u0dda \u0daf\u0dd2\u0d9c <img loading=\"lazy\" decoding=\"async\" width=\"17\" height=\"27\" src=\"\">\u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>II.\u0d89\u0dad\u0dd2\u0dbb\u0dd2 \u0db4\u0dcf\u0daf\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0d9a\u0dd4\u0da9\u0dcf\u0db8 \u0db4\u0dcf\u0daf\u0dba\u0da7 \u0dc0\u0da9\u0dcf &nbsp;\u0d9a\u0dd2\u0db1\u0dca \u0dc0\u0dd0\u0da9\u0dd2 \u0db1\u0db8\u0dca \u0db4\u0dba\u0dd2\u0dad\u0d9c\u0dbb\u0dc3\u0dca \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0db4\u0dcf\u0daf \u0dc0\u0dbd \u0daf\u0dd2\u0d9c\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c \u0d85\u0dad\u0dbb \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>III. \u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca <span class=\"wp-katex-eq\" data-display=\"false\">x^2-5x=4<\/span> &nbsp;\u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>IV&nbsp;\u0dc0\u0dbb\u0dca\u0d9c \u0db4\u0dd6\u0dbb\u0dca\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dc4\u0ddd \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc4\u0ddd \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc0\u0dd2\u0dc3\u0daf\u0dcf \u0d9a\u0dbb\u0dca\u0dab\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>(<span class=\"wp-katex-eq\" data-display=\"false\">\\surd41\\;<\/span>\u0dc4\u0dd2 \u0d85\u0d9c\u0dba 6.4 \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dca\u0db1.)<\/p>\n\n\n\n<p>\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb\u0dd4<\/p>\n\n\n\n<p>(1)<\/p>\n\n\n\n<p>a.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac x{(x-1)}+\\frac{3x}{2(x-1)}=\\frac54<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{2x}{2(x-1)}+\\frac{3x}{2(x-1)}=\\frac54<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{5x}{2(x-1)}=\\frac54<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac x{(x-1)}=\\frac12<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">2x=x-1<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span style=\"text-decoration: underline\">x=-1<\/span><\/p>\n\n\n\n<p>b.<\/p>\n\n\n\n<p>\u0db8\u0dd4\u0dc5\u0dd4 \u0daf\u0dd2\u0d9c = (6x+3) cm<\/p>\n\n\n\n<p>\u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba =<span class=\"wp-katex-eq\" data-display=\"false\">x(6x+3)\\;=\\;6x2\\;+\\;3x\\;<\/span><\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\therefore6x^2+3x=30<\/span>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\therefore2x^2+x=10<\/span>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\">II.<span class=\"wp-katex-eq\" data-display=\"false\">2x^2+x=10<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2x^2+x-10=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2x^2-4x+5x-10=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2x(x-2)+5(x-2)=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">(2x+5)(x-2)=0<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore x=\\frac{-5}2,\\;\\;x=2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">\u0daf\u0dd2\u0d9c \u0dc3\u0dd8\u0dab \u0dc0\u0dd2\u0dba \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0db1\u0dd2\u0dc3\u0dcf;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span style=\"text-decoration: underline\">x=2<\/span><\/p>\n\n\n\n<p>III.\u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba==30cm2<\/p>\n\n\n\n<p>\u0d85\u0dbb\u0dca\u0db0 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<span class=\"wp-katex-eq\" data-display=\"false\">\\frac12\\mathrm\\pi(\\frac{\\mathrm x}2)^2=\\frac12\\times3.14\\times(\\frac12)^2=1.54\\mathrm{cm}^2<\/span><\/p>\n\n\n\n<p>\u0db8\u0dd4\u0dc5\u0dd4 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba= 1.54+30 = <span style=\"text-decoration: underline\">31.54cm<sup>2<\/sup><\/span><\/p>\n\n\n\n<p>(2)<\/p>\n\n\n\n<p>a.<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac3x+\\frac2y=\\frac58\\rightarrow(1)<\/span>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac2x-\\frac1y=\\frac18\\rightarrow(2)<\/span>\n\n\n\n<p>(2)x2<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac4x-\\frac2y=\\frac28\\rightarrow(3)<\/span>\n\n\n\n<p>(1)+(3)<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac3x+\\frac2y+\\frac4x-\\frac2y=\\frac58+\\frac28<\/span>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac7x=\\frac78<\/span>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\frac1x=\\frac18<\/span>\n\n\n\n<p>x=8 <\/p>\n\n\n\n<p>                      X \u0dc4\u0dd2 \u0d85\u0d9c\u0dba (1) \u0da7 \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac38+\\frac2y=\\frac58<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac38+\\frac2y=\\frac58<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac2y=\\frac28<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">Y=8<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore x=8\\;\\;\\;\\;\\;\\;\\;y=8<\/span><\/p>\n\n\n\n<p>b.<\/p>\n\n\n\n<p>I.4x+2 = 2(2x+1)<\/p>\n\n\n\n<p>II.\u0daf\u0ddc\u0da9\u0db8\u0dca \u0d9c\u0dd9\u0da9\u0dd2 \u0dad\u0dd4\u0db1\u0d9a \u0db8\u0dd2\u0dbd&nbsp; = 3x<\/p>\n\n\n\n<p>\u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2 \u0daf\u0dd9\u0d9a\u0d9a \u0db8\u0dd2\u0dbd&nbsp; = 4(2x+1)<\/p>\n\n\n\n<p>\u0db8\u0dd4\u0dc5\u0dd4 \u0db8\u0dd2\u0dbd&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 3x + 4(2x+1)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 11x+ 4<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\therefore11x+4=114<\/span>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 11x = 114-4<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 11x = 110<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X = 10<\/p>\n\n\n\n<p>III.\u0d87\u0db4\u0dbd\u0dca \u0d9c\u0dd9\u0da9\u0dd2\u0dba\u0d9a \u0db8\u0dd2\u0dbd= 2(2x+1)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 2<span class=\"wp-katex-eq\" data-display=\"false\">{(2\\times10)+1}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = <span style=\"text-decoration: underline\">\u0dbb\u0dd4\u0db4\u0dd2\u0dba\u0dbd\u0dca 42<\/span><\/p>\n\n\n\n<p>(3)<\/p>\n\n\n\n<p>PQR \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times(3a+9)\\times3a<\/span><\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times3(a+3)\\times3a<\/span>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac{9a}2(a+3)<\/span>\n\n\n\n<p>PST \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0db1\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times(3a+9)\\times3a<\/span><\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac{9a}2(a+3)<\/span>\n\n\n\n<p>PST \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0db1\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times(a+3)\\times a<\/span><\/p>\n\n\n\n<p>STRQ&nbsp; \u0dad\u0dca\u200d\u0dbb\u0db4\u0dd3\u0dc3\u0dd2\u0dba\u0db8\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba = PQR \u0dc0.\u0db5 \u2013 PST \u0dc0.\u0db5<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">28=\\frac{9a}2(a+3)-\\frac a2(a+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">28=\\frac{9a}2(a+3)-\\frac a2(a+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">28=\\frac a2(a+3)\\times8<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">28=a(a+3)\u00d74<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{28}4=a(a+3)\\times\\frac44<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">7=a^2+3a<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">a^2+3a-7=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-3\\pm\\sqrt{9-4\\times1\\times(-7)}}{2\\times1}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-3\\pm\\sqrt{9+28}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-3\\pm\\sqrt{37}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">SP=\\;\\;\\frac{\\sqrt{37}-3}2<\/span>  (\u0daf\u0dd2\u0d9c \u0dc3\u0dd8\u0dab \u0dc0\u0dd2\u0dba \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca)<\/p>\n\n\n\n<p class=\"has-text-align-center\">PST \u0dc0.\u0db5 <span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12a(a+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times\\frac{(\\surd37-3)}2\\times(\\frac{(\\surd37-3)}2+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times\\frac{(6.08-3)}2\\times(\\frac{(6.08-3}2+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times\\frac{3.08}2\\times(\\frac{3.08}2+3)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">=\\frac12\\times1.54\\times4.54<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">=1.54&#215;2.27<\/p>\n\n\n\n<p class=\"has-text-align-center\">=3.5158 \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a<\/p>\n\n\n\n<p>&nbsp;PST \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0db1\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc0\u0dbb\u0dca\u0d9c \u0d92\u0d9a\u0d9a &nbsp;3 \u0d89\u0d9a\u0dca\u0db8\u0dc0\u0dba\u0dd2<\/p>\n\n\n\n<p>(4)<\/p>\n\n\n\n<p class=\"has-text-align-center\">i)<span class=\"wp-katex-eq\" data-display=\"false\">2(x+3)+2y=40\\;\\rightarrow(1)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2\\times5(x+3)+2y=104\\rightarrow(2)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">ii) (2)-(1)<\/p>\n\n\n\n<p class=\"has-text-align-center\">10(x+3)+2y-2(x+3)-2y=104-40<\/p>\n\n\n\n<p class=\"has-text-align-center\">8(x+3)=64<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{8(x+3)}8=\\frac{64}8<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">x+3=8<\/p>\n\n\n\n<p class=\"has-text-align-center\">x=5<\/p>\n\n\n\n<p>X \u0dc4\u0dd2 \u0d85\u0d9c\u0dba (1) \u0da7 \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca<\/p>\n\n\n\n<p>2(5+3)+2y=40<\/p>\n\n\n\n<p>16+2y=40<\/p>\n\n\n\n<p>2y=24<\/p>\n\n\n\n<p>y=12<\/p>\n\n\n\n<p><span style=\"text-decoration: underline\">\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf x=5 y=12<\/span><\/p>\n\n\n\n<p>iii)<\/p>\n\n\n\n<p>\u0db1\u0dc0 \u0daf\u0dd2\u0d9c =5(5+3)=40 \u0d92\u0d9a\u0d9a<\/p>\n\n\n\n<p><span style=\"text-decoration: underline\">\u0db1\u0dc0 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba =40&#215;12<\/span><\/p>\n\n\n\n<p>(5)<\/p>\n\n\n\n<p>(i)  (x + 3)(x \u2013 1)cm<sup>2<\/sup><\/p>\n\n\n\n<p>(ii)                                                          (x + 3)(x \u2013 1) = 9<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x^2+2x-3=9<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x^2+2x-12=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">(iii) <span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-2\\pm\\sqrt{4-4\\times1(-12)}}{2\\times1}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-2\\pm\\sqrt{52}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-2\\pm2\\sqrt{13}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=-1\\pm\\surd13<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=-1\\pm\\surd13<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=-1\\pm\\;3.6<\/span><\/p>\n\n\n\n<p>\u0daf\u0dd2\u0d9c \u0dc3\u0dd8\u0dab \u0dc0\u0dd2\u0dba \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca x = 2.6 cm<\/p>\n\n\n\n<p>\u0db4\u0dd0\u0dad\u0dca\u0dad\u0d9a \u0daf\u0dd2\u0d9c&nbsp; = 2.6 + 3 =<span style=\"text-decoration: underline\">5.6cm<\/span><\/p>\n\n\n\n<p>(6)<\/p>\n\n\n\n<p>i. 2x \u2013 1<\/p>\n\n\n\n<p>ii.                                                      \u0d89\u0dad\u0dd2\u0dbb\u0dd2 \u0db4\u0dcf\u0daf\u0dda \u0daf\u0dd2\u0d9c&nbsp; = x + 3<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore(2x-1)^2=x^2+(x+3)^2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">4x^2-4x+1=x^2+x^2+6x+9<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2x^2-10x-8=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x^2-5x-4=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">iv.<span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{-5\\pm\\sqrt{(-5)^2-4\\times1(-4)}}{2\\times1}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{5\\pm\\sqrt{25+16}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{5\\pm\\sqrt{41}}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">x=\\frac{5\\pm6.4}2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">\u0daf\u0dd2\u0d9c \u0dc3\u0dd8\u0dab \u0dc0\u0dd2\u0dba \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca <span class=\"wp-katex-eq\" data-display=\"false\">\\therefore x=5.7cm<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">\u0d9a\u0dbb\u0dca\u0dab\u0dba\u0dda \u0daf\u0dd2\u0d9c <span class=\"wp-katex-eq\" data-display=\"false\"><\/span>=2\\times5.7-1<span class=\"wp-katex-eq\" data-display=\"false\"><\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">x=10.4cm<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?id=1Xfd74wulLDsyEulFDtQfKsXzLBEPrVG4&amp;export=download\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0dba\u0dda\u0daf\u0dd3 \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0dad\u0db1\u0da7\u0dba\u0dd2.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?id=1Et8V2zU47bJMKqgyV7zfhq1OvM8J6YG3&amp;export=download\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0dc0\u0dd3\u0da2\u0dd3\u0dba \u0db7\u0dcf\u0d9c \u0dc3\u0dc4\u0dd2\u0dad \u0d92\u0d9a\u0da2 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc3\u0db8\u0d9c\u0dcf\u0db8\u0dd3 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0db7\u0dcf\u0d9c \u0dc3\u0d82\u0d9c\u0dd4\u0dab\u0d9a \u0dc3\u0dc4\u0dd2\u0dad \u0dc3\u0db8\u0d9c\u0dcf\u0db8\u0dd3 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc3\u0dcf\u0db0\u0d9a \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8 \u0dc0\u0dbb\u0dca\u0d9c \u0db4\u0dd6\u0dbb\u0dca\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8 \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dc0\u0dbb\u0dca\u0d9c\u0da1 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8 (1) a.\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1 b.\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba\u0da7 \u0d89\u0da9\u0db8\u0d9a \u0d8d\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dd9\u0dc4\u0dd2 \u0d9a\u0db8\u0dca\u0db6\u0dd2 \u0dc0\u0dd0\u0da7\u0d9a\u0dca \u0db6\u0dd0\u0db3 \u0dc0\u0dd9\u0db1\u0dca\u0d9a\u0dbb \u0d87\u0dad. I.\u0db8\u0dd4\u0dc5\u0dd4 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dcf\u0d9a\u0dcf\u0dbb \u0d9a\u0ddc\u0da7\u0dc3\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba 30cm2 &nbsp;\u0db1\u0db8\u0dca 2&#215;2+ x = 10 \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0db1 [&hellip;]<\/p>\n","protected":false},"author":29,"featured_media":11441,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3787,3623],"tags":[3646,3687,3645,106],"class_list":{"0":"post-11494","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-mathamatics","8":"category-ordinary-level","9":"tag-ganithaya","10":"tag-mathamatics","11":"tag-ol-maths","12":"tag-106"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/11494"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/users\/29"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/comments?post=11494"}],"version-history":[{"count":51,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/11494\/revisions"}],"predecessor-version":[{"id":11759,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/11494\/revisions\/11759"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/media\/11441"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/media?parent=11494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/categories?post=11494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/tags?post=11494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}