College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding: 17

Answer

The solution set is $\left\{0, 64\right\}$.

Work Step by Step

Square both sides to obtain: $x^2=(8\sqrt{x})^2$ Use the rule $(ab)^m = a^mb^m$ to obtain: $x^2=8^2(\sqrt{x})^2 \\x^2=64x$ Subtract $64x$ on both sides of the equation to obtain: $x^2-64=64x-64x \\x^2-64x=0$ Factor out $x$ to obtain: $x(x-64) = 0$ Equate each factor to zero, and then solve each equation to obtain: $\begin{array}{ccc} &x=0 &\text{ or } &x-64=0 \\&x=0 &\text{ or } &x=64 \end{array}$ Thus, the solution set is $\left\{0, 64\right\}$.
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