{"id":235968,"date":"2025-06-15T21:55:05","date_gmt":"2025-06-15T21:55:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235968"},"modified":"2025-06-15T21:55:09","modified_gmt":"2025-06-15T21:55:09","slug":"a-number-is-2-less-than-its-square","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/a-number-is-2-less-than-its-square\/","title":{"rendered":"A number is 2 less than its square."},"content":{"rendered":"\n

A number is 2 less than its square. Find all such numbers.<\/p>\n\n\n\n

Correct Answer:<\/strong><\/p>\n\n\n\n

The numbers that are 2 less than their square are \u20131<\/strong> and 2<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation (<\/strong><\/p>\n\n\n\n

Consider a number represented by a variable, say xxx. The statement “a number is 2 less than its square” can be expressed as a mathematical equation. Translating the statement gives:x=x2\u22122x = x^2 – 2x=x2\u22122<\/p>\n\n\n\n

To solve this equation, rearrange the terms so that the equation equals zero:x2\u2212x\u22122=0x^2 – x – 2 = 0x2\u2212x\u22122=0<\/p>\n\n\n\n

This is a quadratic equation in standard form. Solving such equations can be done using factoring. The goal is to find two numbers that multiply to give \u20132 and add to give \u20131.<\/p>\n\n\n\n

The correct factorization is:(x\u22122)(x+1)=0(x – 2)(x + 1) = 0(x\u22122)(x+1)=0<\/p>\n\n\n\n

Setting each factor equal to zero gives two possible solutions:x\u22122=0\u21d2x=2x – 2 = 0 \\Rightarrow x = 2 x\u22122=0\u21d2x=2x+1=0\u21d2x=\u22121x + 1 = 0 \\Rightarrow x = -1x+1=0\u21d2x=\u22121<\/p>\n\n\n\n

Thus, the two numbers that satisfy the condition are \u20131 and 2.<\/p>\n\n\n\n

Verification of each solution confirms correctness:<\/p>\n\n\n\n

    \n
  • For x=2x = 2x=2: the square is 22=42^2 = 422=4, and the number is 2, which is indeed 2 less than 4.<\/li>\n\n\n\n
  • For x=\u22121x = -1x=\u22121: the square is (\u22121)2=1(-1)^2 = 1(\u22121)2=1, and the number is \u20131, which is also 2 less than 1.<\/li>\n<\/ul>\n\n\n\n

    Both values meet the condition set by the problem statement. The process of solving involved recognizing a quadratic form, factoring accurately, and validating both solutions. The condition “a number is 2 less than its square” is satisfied only by these two values. Therefore, the complete solution set is {\u20131, 2}.<\/p>\n\n\n\n

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

    A number is 2 less than its square. Find all such numbers. Correct Answer: The numbers that are 2 less than their square are \u20131 and 2. Explanation ( Consider a number represented by a variable, say xxx. The statement “a number is 2 less than its square” can be expressed as a mathematical equation. […]<\/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-235968","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235968","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=235968"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235968\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}