{"id":23698,"date":"2021-09-17T15:12:21","date_gmt":"2021-09-17T09:42:21","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=23698"},"modified":"2021-09-17T15:12:25","modified_gmt":"2021-09-17T09:42:25","slug":"01-08q","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/01-08q\/","title":{"rendered":"x \u0dc3\u0db3\u0dc4\u0dcf \u0dad\u0dcf\u0dad\u0dca\u0dc0\u0dd2\u0d9a \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0dca \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1 \u0d94\u0db6\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?"},"content":{"rendered":"\n
<\/div>\n\n\n\n
\n

(x-\\frac1x)^\\frac12+(1-\\frac1x)^\\frac12=x<\/span><\/p>\n\n\n\n

\u0db8\u0dd9\u0db8 \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0dda x \u0dc3\u0db3\u0dc4\u0dcf \u0dad\u0dcf\u0dad\u0dca\u0dc0\u0dd2\u0d9a \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0dca \u0dc3\u0dd9\u0dc0\u0dd3\u0db8\u0dba\u0dd2 \u0d94\u0db6\u0da7 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0d85\u0db7\u0dd2\u0dba\u0ddd\u0d9c\u0dba \u0dc0\u0dd9\u0db1\u0dca\u0db1\u0dda.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

\r\n

\u0d86\u0daf\u0dda\u0dc1\u0db1\u0dba\u0d9a\u0dca \u0dba\u0ddc\u0daf\u0dcf \u0d9c\u0db1\u0dd2\u0db8\u0dd2\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0dca \u0dc3\u0ddc\u0dba\u0db8\u0dd4.<\/strong><\/span><\/p>\r\n

\\left(x\\;-\\;\\frac1x\\right)^{\\frac12\\;}\\;+\\;\\left(1\\;-\\;\\frac1x\\right)^\\frac1{2\\;}\\;=\\;x<\/span><\/p>\r\n<\/div>\n\n\n\n

 <\/p>\r\n

\\begin{array}{l}\\begin{array}{l}\\text{\u0db8\u0dd9\u0dc4\u0dd2}\\;a=\\left(x-\\frac1x\\right)^\\frac12\\;\u0dc3\u0dc4\\;b=\\left(1-\\frac1x\\right)^\\frac12\\text{\u0dbd\u0dd9\u0dc3\u0d9c\u0db1\u0dd2\u0db8\u0dd4}.\\\\\\text{\u0d91\u0dc0\u0dd2\u0da7},\\;a+b=x\\text{\u0dc0\u0dda.}\\end{array}\\\\\\text{\u00d7}\\left(a\\;-\\;b\\right)\\end{array}<\/span><\/p>\r\n\\begin{array}{rcl}\\left(a-b\\right)\\left(a+b\\right)&=&x\\left(a-b\\right)\\\\a^2-b^2&=&x\\left(a-b\\right)-\u2460\\end{array}<\/span>\r\n

 <\/p>\r\n\\begin{array}{rcl}a^2&=&x-\\frac1x\\;\\text{\u0dc3\u0dc4\u00a0}\\;b^2=1-\\frac1x\\;\\text{\u0db1\u0dd2\u0dc3\u0dcf},\\\\&&\\\\\\;\\;\\;\\;a^2-b^2&=&\\left(x-\\frac1x\\right)-\\left(1-\\frac1x\\right)\\\\a^2-b^2&=&x-1\\\\&&\\\\&&\\text{\u0db8\u0dd9\u0dba\u00a0\u2460\u00a0\u0da7\u00a0\u0d86\u0daf\u0dda\u0dc1\u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca,}\\\\&&\\\\x-1&=&x\\left(a-b\\right)\\\\\\frac{\\left(x-1\\right)}x&=&a-b\\\\a-b&=&1-\\frac1x\\;\\;-\\text{\u2461}\\end{array}<\/span>\r\n

 <\/p>\r\n\\begin{array}{rcl}\\text{\u0daf\u0dd0\u0db1\u0dca\u00a0},\\;\\;\\;\\;\\text{\u2461+\u2462\u21d2}2a&=&1-\\frac1x+x\\\\2a&=&\\left(x-\\frac1x\\right)+1\\\\2a&=&a^2+1\\\\0&=&a^2-2a+1\\\\0&=&\\left(a-1\\right){}^2\\;\\;\\;\\\\&&\\therefore a=1\\text{\u0dc0\u0dda.}\\end{array}<\/span>\r\n

 <\/p>\r\n\\begin{array}{rcl}\\text{\u0db1\u0db8\u0dd4\u0dad\u0dca,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}\\operatorname{\u00a0\u00a0\u00a0}a&=&\\left(x-\\frac1x\\right)^\\frac12\\\\\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\therefore1&=&\\left(x-\\frac1x\\right)^\\frac12\\\\x-\\frac1x&=&1^2\\;\\\\\\times x\\;&\\Rightarrow&x(x-\\frac1x)=x\\\\x^2-1&=&x\\\\x^2-x-1&=&0\\end{array}<\/span>\r\n

 <\/p>\r\n\\begin{array}{rcl}&&\\text{\u0db8\u0dd9\u0db8 \u0dc0\u0dbb\u0dca\u0d9c\u0da2 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0dda \u0db8\u0dd6\u0dbd \u0dc3\u0ddc\u0dba\u0db8\u0dd4.}\\\\\\;x&=&\\left(\\frac{1\\pm\\sqrt{1-4\\left(-1\\right)}}2\\right)\\;\\\\x&=&\\;\\left(\\frac{1\\pm\\sqrt5}2\\right)\\\\\\;x&=&\\left(\\frac{1+\\sqrt5}2\\right)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{ \u0dc4\u0ddd\u00a0\u00a0}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;x=\\left(\\frac{1-\\sqrt5}2\\right)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{\u00a0\u00a0\u0dc0\u0dda. }\\;\\\\\\;&=&1.6180\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;=-0.6180\\end{array}<\/span>\r\n

\u0db8\u0dd9\u0db8 \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0dca \u0d89\u0dc4\u0dad \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0da7 \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dbb \u0db6\u0dbd\u0db8\u0dd4.<\/p>\r\n

\r\n

\\left(x\\;-\\;\\frac1x\\right)^{\\frac12\\;}\\;+\\;\\left(1\\;-\\;\\frac1x\\right)^\\frac1{2\\;}\\;=\\;x<\/span><\/p>\r\n<\/div>\r\n

\n\n\n\n<\/p>\r\n\\begin{array}{rcl}x&=&\\left(\\frac{1-\\sqrt5}2\\right)\\;\\text{\u0d86\u0daf\u0dda\u0dc1\u00a0\u0d9a\u0dc5\u00a0\u0dc0\u0dd2\u0da7\u00a0},\\\\\\;LHS&=&2.618\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;RHS=-0.6180\\\\\\;\\therefore\\;\\;\\;LHS\\;&\\neq&RHS\\;\\\\\\therefore\\;\\;\\;\\;\\;\\;x&\\neq&\\left(\\frac{1-\\sqrt5}2\\right)\\;\\;\\\\\\;\\;x&=&\\left(\\frac{1+\\sqrt5}2\\right)\\text{\u00a0\u00a0\u0d86\u0daf\u0dda\u0dc1\u00a0\u0d9a\u0dc5\u00a0\u0dc0\u0dd2\u0da7\u00a0,}\\;\\\\LHS&=&1.6180\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;RHS=1.6180\\\\&&\\;\\therefore\\;\\;\\;LHS=RHS\\;\\\\\\therefore\\;\\;\\;\\;\\;\\;x&=&\\left(\\frac{1+\\sqrt5}2\\right)\\;\\;\\end{array}<\/span>\r\n\\begin{array}{l}\\text{\u0d94\u0db6\u00a0\u0daf\u0db1\u0dca\u0db1\u0dc0\u0dcf\u0daf?}\\\\\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\varphi=\\frac{1+\\sqrt5}2=1.6180\\dots.\\;\\;\\;\\text{\u0db8\u0dd9\u0dba\u00a0\u0dc3\u0dca\u0dc0\u0dbb\u0dca\u0dab\u0db8\u0dba\u00a0\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba\u00a0\u0dba\u0dd2.}\\end{array}<\/span>\r\n

 <\/p>\r\n

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

          \u0db8\u0dd9\u0db8 \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0dca \u0d89\u0dc4\u0dad \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0da7 \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dbb \u0db6\u0dbd\u0db8\u0dd4.  <\/p>\n","protected":false},"author":121,"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-23698","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\/23698"}],"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\/121"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=23698"}],"version-history":[{"count":46,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/23698\/revisions"}],"predecessor-version":[{"id":29692,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/23698\/revisions\/29692"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=23698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=23698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=23698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}