{"id":267957,"date":"2025-07-23T18:07:52","date_gmt":"2025-07-23T18:07:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=267957"},"modified":"2025-07-23T18:07:57","modified_gmt":"2025-07-23T18:07:57","slug":"solve-the-equation-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/solve-the-equation-4\/","title":{"rendered":"Solve the equation"},"content":{"rendered":"\n

Solve the equation: 9x^4 – 37x^2 + 4 = 0<\/p>\n\n\n\n

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

We are given the equation:9×4\u221237×2+4=09x^4 – 37x^2 + 4 = 09×4\u221237×2+4=0<\/p>\n\n\n\n

To solve it, we can start by making a substitution to simplify the equation. Let:y=x2y = x^2y=x2<\/p>\n\n\n\n

This substitution transforms the equation into a quadratic form in terms of yyy:9y2\u221237y+4=09y^2 – 37y + 4 = 09y2\u221237y+4=0<\/p>\n\n\n\n

Now, we can solve this quadratic equation using the quadratic formula. The quadratic formula is given by:y=\u2212b\u00b1b2\u22124ac2ay = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}y=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n

For our equation, a=9a = 9a=9, b=\u221237b = -37b=\u221237, and c=4c = 4c=4. Substituting these values into the quadratic formula:y=\u2212(\u221237)\u00b1(\u221237)2\u22124(9)(4)2(9)y = \\frac{-(-37) \\pm \\sqrt{(-37)^2 – 4(9)(4)}}{2(9)}y=2(9)\u2212(\u221237)\u00b1(\u221237)2\u22124(9)(4)\u200b\u200b<\/p>\n\n\n\n

Simplifying the expression:y=37\u00b11369\u221214418y = \\frac{37 \\pm \\sqrt{1369 – 144}}{18}y=1837\u00b11369\u2212144\u200b\u200by=37\u00b1122518y = \\frac{37 \\pm \\sqrt{1225}}{18}y=1837\u00b11225\u200b\u200by=37\u00b13518y = \\frac{37 \\pm 35}{18}y=1837\u00b135\u200b<\/p>\n\n\n\n

This gives two possible solutions for yyy:y=37+3518=7218=4y = \\frac{37 + 35}{18} = \\frac{72}{18} = 4y=1837+35\u200b=1872\u200b=4<\/p>\n\n\n\n

ory=37\u22123518=218=19y = \\frac{37 – 35}{18} = \\frac{2}{18} = \\frac{1}{9}y=1837\u221235\u200b=182\u200b=91\u200b<\/p>\n\n\n\n

Now, recall that y=x2y = x^2y=x2, so we have two possible equations to solve for xxx:<\/p>\n\n\n\n

    \n
  1. x2=4x^2 = 4×2=4<\/li>\n\n\n\n
  2. x2=19x^2 = \\frac{1}{9}x2=91\u200b<\/li>\n<\/ol>\n\n\n\n

    For the first equation, x2=4x^2 = 4×2=4, we take the square root of both sides:x=\u00b12x = \\pm 2x=\u00b12<\/p>\n\n\n\n

    For the second equation, x2=19x^2 = \\frac{1}{9}x2=91\u200b, we take the square root of both sides:x=\u00b113x = \\pm \\frac{1}{3}x=\u00b131\u200b<\/p>\n\n\n\n

    Thus, the solutions to the original equation are:x=2,\u2009x=\u22122,\u2009x=13,\u2009x=\u221213x = 2, \\, x = -2, \\, x = \\frac{1}{3}, \\, x = -\\frac{1}{3}x=2,x=\u22122,x=31\u200b,x=\u221231\u200b<\/p>\n\n\n\n

    So, the solutions to the equation 9×4\u221237×2+4=09x^4 – 37x^2 + 4 = 09×4\u221237×2+4=0 are:x=2,\u2009x=\u22122,\u2009x=13,\u2009x=\u221213x = 2, \\, x = -2, \\, x = \\frac{1}{3}, \\, x = -\\frac{1}{3}x=2,x=\u22122,x=31\u200b,x=\u221231\u200b<\/p>\n\n\n\n

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

    Solve the equation: 9x^4 – 37x^2 + 4 = 0 The Correct Answer and Explanation is: We are given the equation:9×4\u221237×2+4=09x^4 – 37x^2 + 4 = 09×4\u221237×2+4=0 To solve it, we can start by making a substitution to simplify the equation. Let:y=x2y = x^2y=x2 This substitution transforms the equation into a quadratic form in terms […]<\/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-267957","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267957","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=267957"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267957\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=267957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=267957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=267957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}