{"id":29664,"date":"2021-09-17T14:41:45","date_gmt":"2021-09-17T09:11:45","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=29664"},"modified":"2021-09-17T14:41:50","modified_gmt":"2021-09-17T09:11:50","slug":"01-07q","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/01-07q\/","title":{"rendered":"\u0db4\u0dd4\u0d82\u0da0\u0dd2 \u0d85\u0db7\u0dd2\u0dba\u0ddd\u0d9c\u0dba\u0d9a\u0dca!"},"content":{"rendered":"\n
<\/div>\n\n\n\n
\n

a, b, \u0dc4\u0dcf c \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0d91\u0d9a\u0dca \u0d91\u0d9a\u0dca \u0db4\u0dcf\u0daf\u0dba\u0dda \u0daf\u0dd2\u0d9c\u0dc0\u0dbd\u0dca \u0dba\u0dd0\u0dba\u0dd2 \u0dc3\u0dbd\u0d9a\u0db8\u0dd4. ab + bc + ca = 1 \u0dbd\u0dd9\u0dc3 \u0daf\u0dd3 \u0d87\u0dad.<\/strong><\/p>\n\n\n\n

( a +1 )(b +1 )(c +1 ) < 4 \u0dc0\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

<\/p>\n<\/div><\/div>\n\n\n\n

\u0db8\u0dd9\u0dc0\u0dd0\u0db1\u0dd2 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba \u0d85\u0db4\u0dd2 \u0daf\u0dd0\u0db1\u0dca \u0db6\u0dbd\u0db8\u0dd4.<\/p>\n\n\n\n

\u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8 ( a +1 )(b +1 )(c +1 ) \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dcf\u0dbb\u0dab\u0dba \u0d9a\u0dbb\u0dbd\u0dcf \u0dbd\u0dd2\u0dba\u0dcf \u0d9c\u0db8\u0dd4.<\/p>\n\n\n\n

( a +1 )(b +1 )(c +1 ) = abc + ( ab + bc + ac ) + a +b + c + 1<\/p>\n\n\n\n

ab + bc + ca = 1 \u0db1\u0dd2\u0dc3\u0dcf,
= abc + 1 + a + b + c + 1
= abc + a + b + c + 2<\/p>\n\n\n\n

\u0d8a\u0dbd\u0d9f\u0da7 ( a – 1 )( b -1 )(c -1 ) \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dcf\u0dbb\u0dab\u0dba \u0d9a\u0dbb\u0dbd\u0dcf \u0dbd\u0dd2\u0dba\u0dcf \u0d9c\u0db8\u0dd4.<\/p>\n\n\n\n

\\begin{array}{rcl}(\\;a\\;-\\;1\\;)(\\;b\\;-1\\;)(c\\;-1\\;)\\\\&=&\\;abc\\;-\\;(\\;ab\\;+\\;bc\\;+\\;ac\\;)\\;+\\;a\\;+b\\;+\\;c\\;\u2013\\;1\\\\&=&\\;abc\\;-\\;1\\;+\\;a\\;+\\;b\\;+\\;c\\;\u2013\\;1\\\\&=&\\;abc\\;+\\;a\\;+\\;b\\;+\\;c\\;\u2013\\;2\\\\(\\;a\\;-\\;1\\;)(\\;b\\;-1\\;)(c\\;-1\\;)\\;&=&\\;(\\;a\\;+1\\;)(b\\;+1\\;)(c\\;+1\\;)\\;\u2013\\;4\\end{array}<\/span><\/p>\n\n\n\n

\u0d92 \u0d85\u0db1\u0dd4\u0dc0 , ( a +1 )(b +1 )(c +1 ) < 4 \u0dc0\u0dd3\u0db8\u0da7 \u0db1\u0db8\u0dca, ( a – 1 )( b -1 )(c -1 ) < 0 \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/p>\n\n\n\n

a, b, c \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0db4\u0dcf\u0daf\u0dc0\u0dbd \u0daf\u0dd2\u0d9c\u0dc0\u0dbd\u0dca \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf a, b, c > 0 \u0dc0\u0dda.<\/p>\n\n\n\n

( a – 1 )( b -1 )(c -1 ) < 0 \u0dc0\u0dd3\u0db8\u0da7 \u0db1\u0db8\u0dca \u0dad\u0dc0\u0daf\u0dd4\u0dbb\u0da7\u0dad\u0dca,  a, b, c < 1 \u0dc0\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\n\n\n\n

\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0d91\u0d9a\u0dca \u0db4\u0dcf\u0daf\u0dba\u0d9a \u0daf\u0dd2\u0d9c \u0d85\u0db1\u0dd9\u0d9a\u0dca \u0db4\u0dcf\u0daf \u0daf\u0dd9\u0d9a\u0dda \u0d91\u0d9a\u0dad\u0dd4\u0dc0\u0da7 \u0dc0\u0da9\u0dcf \u0d9a\u0dd4\u0da9\u0dcf \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf,
0 \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/p>\n\n\n\n

a, b, c \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0db4\u0dcf\u0daf\u0dc0\u0dbd \u0daf\u0dd2\u0d9c\u0dc0\u0dbd\u0dca \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf a, b, c > 0 \u0dc0\u0dda.<\/p>\n\n\n\n

                                           \\begin{array}{rcl}c\\;\\;&<&\\;\\;a\\;\\;+\\;\\;b\\\\c^2&<&ac\\;+\\;bc\\\\c^2&<&1\\;\u2013\\;ab\\end{array}<\/span> <\/p>\n\n\n\n

ab \u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba + \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf , 1 \u2013 ab < 1 \u0dc0\u0dda. \u2234 c < 1 \u0dc0\u0dda.<\/p>\n\n\n\n

\u0d91\u0dbd\u0dd9\u0dc3\u0db8, b < 1 \u0dc4\u0dcf a < 1 \u0dc0\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0dd2\u0dba \u0dc4\u0dd0\u0d9a.<\/p>\n\n\n\n

\u0d92 \u0d85\u0db1\u0dd4\u0dc0, 0 < a,b,c < 1 \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf, ( a +1 )(b +1 )(c +1 ) < 4 \u0dc0\u0db1 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0dd2\u0dba \u0dc4\u0dd0\u0d9a.<\/p>\n\n\n\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u0db8\u0dd9\u0dc0\u0dd0\u0db1\u0dd2 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba \u0d85\u0db4\u0dd2 \u0daf\u0dd0\u0db1\u0dca \u0db6\u0dbd\u0db8\u0dd4. \u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8 ( a +1 )(b +1 )(c +1 ) \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dcf\u0dbb\u0dab\u0dba \u0d9a\u0dbb\u0dbd\u0dcf \u0dbd\u0dd2\u0dba\u0dcf \u0d9c\u0db8\u0dd4. ( a +1 )(b +1 )(c +1 ) = abc + ( ab + bc + ac ) + a +b + c + 1 ab + bc + ca = 1 \u0db1\u0dd2\u0dc3\u0dcf, = abc […]<\/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-29664","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\/29664"}],"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=29664"}],"version-history":[{"count":7,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/29664\/revisions"}],"predecessor-version":[{"id":29677,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/29664\/revisions\/29677"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=29664"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=29664"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=29664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}