{"id":2752,"date":"2023-02-11T07:28:44","date_gmt":"2023-02-11T07:28:44","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2752"},"modified":"2023-02-20T19:54:59","modified_gmt":"2023-02-20T19:54:59","slug":"un-sistema-y-un-eneagono","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2023\/02\/11\/un-sistema-y-un-eneagono\/","title":{"rendered":"Un sistema y un ene\u00e1gono"},"content":{"rendered":"<pre>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2023 (viernes ma\u00f1ana)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Decimos que una terna (a, b, c) de n\u00fameros reales todos distintos de cero, es local, si:<\/p>\n<p>a\u00b2 + a = b\u00b2<\/p>\n<p>b\u00b2 + b = c\u00b2<\/p>\n<p>c\u00b2 + c = a\u00b2.<\/p>\n<p>(a) Probar que, si (a, b, c) es local, entonces (a \u2013 b)(b \u2013 c)(c \u2013 a) = 1.<\/p>\n<p>(b) Sea A\u2081 A\u2082 \u2026 A\u2089 un ene\u00e1gono regular (pol\u00edgono regular de 9 lados). Supongamos que |A\u2081A\u2084| = 1 y sea |A\u2081A\u2082| = a, |A\u2081A\u2083| = b y |A\u2081A\u2085| = c. Prueba que (a, b, -c) es local.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/284.sistema.png\" alt=\"\" width=\"300\" height=\"300\" class=\"alignnone size-full wp-image-2753\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/284.sistema.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/284.sistema-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2023\/02\/18\/solucion-a-un-sistema-y-un-eneagono\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2023 (viernes ma\u00f1ana) Se dirige a una edad de: 16-17 a\u00f1os Decimos que una terna (a, b, c) de n\u00fameros reales todos distintos de cero, es local, si: a\u00b2 + a = b\u00b2 b\u00b2 + b = c\u00b2 c\u00b2 + c = a\u00b2. [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2849],"tags":[],"class_list":["post-2752","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2752","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=2752"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2752\/revisions"}],"predecessor-version":[{"id":2767,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2752\/revisions\/2767"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2752"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2752"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2752"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}