{"id":144519,"date":"2024-09-24T19:41:32","date_gmt":"2024-09-24T19:41:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144519"},"modified":"2024-09-24T20:58:53","modified_gmt":"2024-09-24T20:58:53","slug":"numeros-que-multiplicados-den-30-y-sumados-o-restados-den-11","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/numeros-que-multiplicados-den-30-y-sumados-o-restados-den-11\/","title":{"rendered":"Numeros que multiplicados den 30 y sumados o restados den -11"},"content":{"rendered":"\n

Numeros que multiplicados den 30 y sumados o restados den -11<\/p>\n\n\n\n

The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Para encontrar dos n\u00fameros que multiplicados den 30 y que, al sumarlos o restarlos, den -11, vamos a plantear el problema de la siguiente manera:<\/p>\n\n\n\n

    \n
  1. Definici\u00f3n de las variables<\/strong>: Sea xxx y yyy los dos n\u00fameros que buscamos.<\/li>\n\n\n\n
  2. Planteamiento de las ecuaciones<\/strong>:\n
      \n
    • La primera ecuaci\u00f3n corresponde al producto:
      x\u22c5y=30x \\cdot y = 30x\u22c5y=30<\/li>\n\n\n\n
    • La segunda ecuaci\u00f3n corresponde a la suma o resta, y en este caso consideraremos la suma para obtener -11: x+y=\u221211x + y = -11x+y=\u221211<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Resolviendo las ecuaciones<\/strong>: A partir de la segunda ecuaci\u00f3n, podemos despejar yyy: y=\u221211\u2212xy = -11 – xy=\u221211\u2212x Ahora sustituimos yyy en la primera ecuaci\u00f3n: x\u22c5(\u221211\u2212x)=30x \\cdot (-11 – x) = 30x\u22c5(\u221211\u2212x)=30 Esto se simplifica a: \u221211x\u2212x2=30-11x – x^2 = 30\u221211x\u2212x2=30 Reordenando la ecuaci\u00f3n, obtenemos: x2+11x+30=0x^2 + 11x + 30 = 0x2+11x+30=0<\/li>\n\n\n\n
    • Factorizaci\u00f3n<\/strong>: Buscamos factores de 30 que sumen 11. Los n\u00fameros que cumplen con esto son 5 y 6, pero como deben ser negativos para que su suma sea -11, podemos expresar la ecuaci\u00f3n factorizada como: (x+5)(x+6)=0(x + 5)(x + 6) = 0(x+5)(x+6)=0<\/li>\n\n\n\n
    • Soluciones<\/strong>: De esta factorizaci\u00f3n, encontramos las ra\u00edces: x+5=0\u21d2x=\u22125x + 5 = 0 \\quad \\Rightarrow \\quad x = -5x+5=0\u21d2x=\u22125 x+6=0\u21d2x=\u22126x + 6 = 0 \\quad \\Rightarrow \\quad x = -6x+6=0\u21d2x=\u22126<\/li>\n<\/ol>\n\n\n\n

      Por lo tanto, los dos n\u00fameros que buscamos son -5 y -6. Verificamos que:<\/p>\n\n\n\n

        \n
      • Al multiplicarlos: \u22125\u22c5\u22126=30-5 \\cdot -6 = 30\u22125\u22c5\u22126=30<\/li>\n\n\n\n
      • Al sumarlos: \u22125+(\u22126)=\u221211-5 + (-6) = -11\u22125+(\u22126)=\u221211<\/li>\n<\/ul>\n\n\n\n

        Conclusi\u00f3n<\/strong>: Los n\u00fameros que multiplicados dan 30 y sumados dan -11 son -5 y -6. Esta soluci\u00f3n se obtiene a trav\u00e9s del an\u00e1lisis algebraico, utilizando el m\u00e9todo de factorizaci\u00f3n, que nos permite hallar n\u00fameros que satisfacen las condiciones planteadas en el problema.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Numeros que multiplicados den 30 y sumados o restados den -11 The Correct answer and Explanation is: Para encontrar dos n\u00fameros que multiplicados den 30 y que, al sumarlos o restarlos, den -11, vamos a plantear el problema de la siguiente manera: Por lo tanto, los dos n\u00fameros que buscamos son -5 y -6. Verificamos […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-144519","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144519","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=144519"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144519\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144519"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}