{"id":22236,"date":"2021-08-04T21:22:30","date_gmt":"2021-08-04T15:52:30","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=22236"},"modified":"2021-09-12T15:56:43","modified_gmt":"2021-09-12T10:26:43","slug":"02-05q1","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/02-05q1\/","title":{"rendered":"\u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dad\u0dd2\u0dba\u0dd9\u0db1 \u0db8\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc0\u0dd2\u0dc3\u0db3\u0dbd\u0dcf(x+y)2 \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0dbd\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf \u0db6\u0dbd\u0db1\u0dca\u0db1."},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\"><\/div>\n\n\n\n<div class=\"wp-block-cover has-background-dim\" style=\"background-color:#e0c8f8;min-height:111px;aspect-ratio:unset;\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#000532;font-size:14px\"><span class=\"wp-katex-eq\" data-display=\"false\">(x+\\sqrt{1+x^2})(y+\\sqrt{1+y^2})\\;=\\;1<\/span><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-cover has-white-background-color has-background-dim\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-black-color has-white-background-color has-text-color has-background\">\u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0daf\u0dd0\u0d9a\u0dca\u0d9a\u0db8 \u0db6\u0dba \u0dc4\u0dd2\u0dad\u0dd4\u0dab\u0daf?\u0d9c\u0dcf\u0dab \u0dc4\u0daf\u0db1\u0dca\u0db1\u0dda \u0d9a\u0ddc\u0dc4\u0ddc\u0db8\u0daf \u0d9a\u0dd2\u0dba\u0dbd\u0dcf \u0dad\u0dcf\u0db8 \u0d9a\u0dbd\u0dca\u0db4\u0db1\u0dcf \u0d9a\u0dbb\u0db1\u0dc0\u0daf?<\/p>\n\n\n\n<p class=\"has-black-color has-white-background-color has-text-color has-background\">\u0d92 \u0dc0\u0d9c\u0dda \u0dc0\u0dd9\u0dbd\u0dcf\u0dc0\u0da7 \u0d9a\u0dbb\u0db1\u0dca\u0db1 \u0d95\u0db1 \u0d91\u0d9a\u0dca \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0d9a\u0da7 \u0d85\u0daf\u0dcf\u0dc5 \u0db4\u0daf\u0dba\u0db8 \u0dad\u0db1\u0dd2 \u0db4\u0daf\u0dba\u0d9a\u0dca \u0d9a\u0dbb\u0d9c\u0dd9\u0db1 \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dad\u0dcf\u0dc0\u0d9a\u0dca \u0d9c\u0ddc\u0da9\u0db1\u0d9c\u0dcf \u0d9c\u0db1\u0dca\u0db1 \u0d91\u0d9a. \u0daf\u0dd0\u0d9a\u0dca\u0d9a \u0d9c\u0db8\u0db1\u0dca \u0d85\u0db8\u0dcf\u0dbb\u0dd4 \u0dc0\u0d9c\u0dda \u0db4\u0dd9\u0db1\u0dd4\u0dab\u0da7 \u0db8\u0dda \u0d9c\u0dcf\u0dab \u0dbd\u0dda\u0dc3\u0dd2\u0dba\u0dd9\u0db1\u0dca\u0db8 \u0dc4\u0daf\u0db1\u0dca\u0db1\u0dda \u0d9a\u0ddc\u0dc4\u0ddc\u0db8\u0daf \u0d9a\u0dd2\u0dba\u0dbd \u0db6\u0dbd\u0db8\u0dd4\u0daf?<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-white-background-color has-text-color has-background\"><span class=\"wp-katex-eq\" data-display=\"false\">(x+\\sqrt{1+x^2})\\;=u<\/span> &nbsp;\u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4. \u0d91\u0dc0\u0dd2\u0da7,<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-white-background-color has-text-color has-background\"><span class=\"wp-katex-eq\" data-display=\"false\">(x+\\sqrt{1+x^2})(y+\\sqrt{1+y^2})\\;=\\;1<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-white-background-color has-text-color has-background\"><span class=\"wp-katex-eq\" data-display=\"false\">u\\;(y+\\sqrt{1+y^2})\\;=\\;1<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">(y+\\sqrt{1+y^2})\\;=\\;\\frac1u<\/span>&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt{1+y^2}\\;=\\;\\frac1u-\\;y<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">1+y^2\\;=(\\frac1u-\\;y)^2<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">1+y^2\\;=\\frac1{u^2}-\\;\\frac{2y}u+y^2<\/span>&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{2y}u=\\frac1{u^2}-\\;1<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">2y=\\frac1u-\\;u<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">y=\\frac12(-2x)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">y=(-x)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">y+x\\;=0<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">(y+x)^2\\;=0<\/span><br><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1u=\\;\\frac1{(x+\\sqrt{1+x^2})}\\times(\\frac{x-\\sqrt{1+x^2}}{x-\\sqrt{1+x^2}})<\/span> <sup>&nbsp;<\/sup><br><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1u=\\;\\frac{(x-\\sqrt{1+x^2)}}{x^2-(1+x^2)}<\/span><br><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1u=\\;\\sqrt{1+x^{2\\;}}-\\;x<\/span><br><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1u-u=\\;(\\sqrt{1+x^{2\\;}}-\\;x)-(x+\\sqrt{1+x^2})<\/span><br><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1u-u=(-2\\;x)<\/span><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp;<\/p>\n","protected":false},"author":73,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[6067,42,3629],"tags":[],"class_list":{"0":"post-22236","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-infinite-thinking","7":"category-advanced-level-science","8":"category-combined-mathematics"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/22236"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/73"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=22236"}],"version-history":[{"count":11,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/22236\/revisions"}],"predecessor-version":[{"id":25048,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/22236\/revisions\/25048"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=22236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=22236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=22236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}