{"id":271584,"date":"2025-07-26T04:40:01","date_gmt":"2025-07-26T04:40:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271584"},"modified":"2025-07-26T04:40:03","modified_gmt":"2025-07-26T04:40:03","slug":"in-the-given-equation-c-is-a-positive-constant","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/in-the-given-equation-c-is-a-positive-constant\/","title":{"rendered":"In the given equation, c is a positive constant."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

One of the solutions to the given equation is x = sqrt(1521 + c^2). The other possible solution is x = -sqrt(1521 + c^2).<\/p>\n\n\n\n

To find the solutions to the equation x^2 \/ sqrt(x^2 – c^2) = c^2 \/ sqrt(x^2 – c^2) + 39, we can begin by simplifying the expression. The first step involves consolidating the terms that contain the variable x and the constant c. Both fractions in the equation share a common denominator, which is sqrt(x^2 – c^2). This structure suggests that we can simplify the equation by moving the term c^2 \/ sqrt(x^2 – c^2) to the left side. We do this by subtracting it from both sides of the equation, which results in the following:<\/p>\n\n\n\n

x^2 \/ sqrt(x^2 – c^2) – c^2 \/ sqrt(x^2 – c^2) = 39<\/p>\n\n\n\n

Now that the terms with the common denominator are on the same side, we can combine them into a single fraction:<\/p>\n\n\n\n

(x^2 – c^2) \/ sqrt(x^2 – c^2) = 39<\/p>\n\n\n\n

The expression on the left side can be simplified using the rules of exponents. The numerator is x^2 – c^2, and the denominator is the square root of that same expression. An expression divided by its square root simplifies to the square root of that expression. For example, A \/ sqrt(A) = sqrt(A). Applying this rule, our equation becomes much simpler:<\/p>\n\n\n\n

sqrt(x^2 – c^2) = 39<\/p>\n\n\n\n

To isolate the variable x, we must first eliminate the square root. This is accomplished by squaring both sides of the equation:<\/p>\n\n\n\n

(sqrt(x^2 – c^2))^2 = 39^2
x^2 – c^2 = 1521<\/p>\n\n\n\n

Next, we add c^2 to both sides of the equation to isolate the x^2 term:<\/p>\n\n\n\n

x^2 = 1521 + c^2<\/p>\n\n\n\n

Finally, we solve for x by taking the square root of both sides. When taking a square root in this context, we must account for both the positive and negative roots:<\/p>\n\n\n\n

x = \u00b1sqrt(1521 + c^2)<\/p>\n\n\n\n

This gives two distinct solutions for x. One solution is the positive root, x = sqrt(1521 + c^2), and the other is the negative root, x = -sqrt(1521 + c^2). The problem asks for one of the solutions, so either of these is a correct answer. It is also important to note that for the original equation to be defined, the term inside the square root, x^2 – c^2, must be greater than zero. Our solutions satisfy this condition, as x^2 = 1521 + c^2, which is inherently greater than c^2.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: One of the solutions to the given equation is x = sqrt(1521 + c^2). The other possible solution is x = -sqrt(1521 + c^2). To find the solutions to the equation x^2 \/ sqrt(x^2 – c^2) = c^2 \/ sqrt(x^2 – c^2) + 39, we can begin by simplifying the expression. The […]<\/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-271584","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271584","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=271584"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271584\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}