{"id":2370,"date":"2022-02-26T09:40:01","date_gmt":"2022-02-26T09:40:01","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2370"},"modified":"2022-03-19T07:16:49","modified_gmt":"2022-03-19T07:16:49","slug":"igualdad-y-conclusion","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2022\/02\/26\/igualdad-y-conclusion\/","title":{"rendered":"Igualdad y conclusi\u00f3n"},"content":{"rendered":"<pre>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2022 (viernes ma\u00f1ana)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Sean a<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub>, a<sub>4<\/sub>, a<sub>5<\/sub> y a<sub>6<\/sub> n\u00fameros reales diferentes, de manera que ninguno de ellos es igual a 0.<\/p>\n<p>Supongamos que (a<sub>1<\/sub>\u00b2 + a<sub>2<\/sub>\u00b2 + a<sub>3<\/sub>\u00b2 + a<sub>4<\/sub>\u00b2 + a<sub>5<\/sub>\u00b2)(a<sub>2<\/sub>\u00b2 + a<sub>3<\/sub>\u00b2 + a<sub>4<\/sub>\u00b2 + a<sub>5<\/sub>\u00b2 + a<sub>6<\/sub>\u00b2) = (a<sub>1<\/sub>a<sub>2<\/sub> + a<sub>2<\/sub>a<sub>3<\/sub> +a<sub>3<\/sub>a<sub>4<\/sub> + a<sub>4<\/sub>a<sub>5<\/sub> + a<sub>5<\/sub>a<sub>6<\/sub>)\u00b2.<\/p>\n<p>Demuestra que los n\u00fameros  a<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub>, a<sub>4<\/sub>, a<sub>5<\/sub> y a<sub>6<\/sub> est\u00e1n en progresi\u00f3n geom\u00e9trica.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2022\/02\/236.Igualdad.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-2371\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2022\/02\/236.Igualdad.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2022\/02\/236.Igualdad-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2022\/03\/05\/solucion-a-igualdad-y-conclusion\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2022 (viernes ma\u00f1ana) Se dirige a una edad de: 16-17 a\u00f1os Sean a1, a2, a3, a4, a5 y a6 n\u00fameros reales diferentes, de manera que ninguno de ellos es igual a 0. Supongamos que (a1\u00b2 + a2\u00b2 + a3\u00b2 + a4\u00b2 + a5\u00b2)(a2\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-2370","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\/2370","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=2370"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2370\/revisions"}],"predecessor-version":[{"id":2398,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2370\/revisions\/2398"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}