{"id":3259,"date":"2021-02-14T18:00:02","date_gmt":"2021-02-14T18:00:02","guid":{"rendered":"https:\/\/presswiki.allmath.gr\/wpwiki18\/?p=3259"},"modified":"2021-02-14T18:00:48","modified_gmt":"2021-02-14T18:00:48","slug":"2021031443290-%ce%b5%ce%be%ce%af%cf%83%cf%89%cf%83%ce%b7-%ce%ba%ce%b1%ce%b9-%cf%80%ce%b1%cf%81%ce%ac%cf%83%cf%84%ce%b1%cf%83%ce%b7","status":"publish","type":"post","link":"https:\/\/presswiki.allmath.gr\/wpwiki18\/2021\/02\/14\/18\/00\/02\/3259\/","title":{"rendered":"2021031443290- \u0395\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7."},"content":{"rendered":"\n<p><a href=\"https:\/\/mathematica.gr\/forum\/viewtopic.php?f=27&amp;t=69043&amp;fbclid=IwAR2mp_qmhIRqagKe7JOcNT_0G639jGd_7TCqXrisfX3NC7LBsCf12IidHUU#p335779\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/mathematica.gr\/forum\/viewtopic.php?f=27&amp;t=69043&amp;fbclid=IwAR2mp_qmhIRqagKe7JOcNT_0G639jGd_7TCqXrisfX3NC7LBsCf12IidHUU#p335779<\/a><\/p>\n\n\n\n<p>\u0388\u03c3\u03c4\u03c9 $a, b, c$ \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 $x^3-x-1=0$.<br>\u039d\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b9\u03bc\u03ae \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7\u03c2:<br>$\\frac{1-a}{1+a}+\\frac{1-b}{1+b}+\\frac{1-c}{1+c}$<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img width=\"345\" height=\"82\" src=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/02\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-53.png\" alt=\"\" class=\"wp-image-3260\" srcset=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/02\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-53.png 345w, https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/02\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-53-300x71.png 300w\" sizes=\"(max-width: 345px) 85vw, 345px\" \/><\/figure>\n\n\n\n<p>\u0398\u03ad\u03c4\u03bf\u03c5\u03bc\u03b5 $t= \\dfrac {1-x}{1+x}\\,(<em>)$ , \u03cc\u03c0\u03bf\u03c5 $x$ \u03c1\u03af\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03b4\u03bf\u03b8\u03b5\u03af\u03c3\u03b1\u03c2 \u03c4\u03c1\u03b9\u03c4\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1\u03c2. \u039b\u03cd\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd $(<\/em>)$ \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 $x$ \u03b8\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 $x= \\dfrac {1-t}{1+t}$, \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b8\u03ad\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03c4\u03b7\u03bd \u03c4\u03c1\u03b9\u03c4\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/p>\n\n\n\n<p>$\\displaystyle{\\left ( \\dfrac {1-t}{1+t}\\right )^3- \\dfrac {1+t}{1-t} -1 =0}$<\/p>\n\n\n\n<p>\u03a0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b5\u03c0\u03af \\((1-t)^3\\) \u03b8\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bc\u03b5\u03c4\u03ac \u03c4\u03b9\u03c2 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 $t^3-t^2+7t+1=0$. \u0391\u03c0\u03cc Vieta \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd \u03c4\u03b7\u03c2 \u03c4\u03b5\u03bb\u03b5\u03c5\u03b1\u03c4\u03af\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 $1$. \u0391\u03bb\u03bb\u03ac \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd $(*)$ \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 $\\displaystyle{ \\dfrac {1-a}{1+a}, \\, \\dfrac {1-b}{1+b},\\, \\dfrac {1-c}{1+c}}$. \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2<\/p>\n\n\n\n<p>$\\displaystyle{ \\dfrac {1-a}{1+a}+ \\dfrac {1-b}{1+b}+ \\dfrac {1-c}{1+c}=1}$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/mathematica.gr\/forum\/viewtopic.php?f=27&amp;t=69043&amp;fbclid=IwAR2mp_qmhIRqagKe7JOcNT_0G639jGd_7TCqXrisfX3NC7LBsCf12IidHUU#p335779 \u0388\u03c3\u03c4\u03c9 $a, b, c$ \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 $x^3-x-1=0$.\u039d\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b9\u03bc\u03ae \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7\u03c2:$\\frac{1-a}{1+a}+\\frac{1-b}{1+b}+\\frac{1-c}{1+c}$ \u0398\u03ad\u03c4\u03bf\u03c5\u03bc\u03b5 $t= \\dfrac {1-x}{1+x}\\,()$ , \u03cc\u03c0\u03bf\u03c5 $x$ \u03c1\u03af\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03b4\u03bf\u03b8\u03b5\u03af\u03c3\u03b1\u03c2 \u03c4\u03c1\u03b9\u03c4\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1\u03c2. \u039b\u03cd\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd $()$ \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 $x$ \u03b8\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 $x= \\dfrac {1-t}{1+t}$, \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b8\u03ad\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03c4\u03b7\u03bd \u03c4\u03c1\u03b9\u03c4\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 $\\displaystyle{\\left ( \\dfrac {1-t}{1+t}\\right )^3- \\dfrac {1+t}{1-t} -1 =0}$ \u03a0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b5\u03c0\u03af \\((1-t)^3\\) \u03b8\u03b1 &hellip; <a href=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/2021\/02\/14\/18\/00\/02\/3259\/\" class=\"more-link\">\u0394\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1<span class=\"screen-reader-text\"> &#8220;2021031443290- \u0395\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7.&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/3259"}],"collection":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/comments?post=3259"}],"version-history":[{"count":2,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/3259\/revisions"}],"predecessor-version":[{"id":3262,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/3259\/revisions\/3262"}],"wp:attachment":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/media?parent=3259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/categories?post=3259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/tags?post=3259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}