Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.6 - Rational Equations - Exercise Set - Page 463: 35


Solution set: $\{4,10\}$

Work Step by Step

$g(a)=7$ $\displaystyle \frac{a}{2}+\frac{20}{a}=7$ Exclude solutions which yield 0 in denominators: $a\neq 0\qquad (*)$ Multiply the equation with the LCD=$2a$ $a^{2}+40=14a$ $a^{2}-14a+40=0$ ... $(x^{2}+bx+c$ is factored by searching for factors of c whose sum is b). ... -10 and -4 are factors of 40 whose sum is -14 $(a-10)(a-4)=0$ By the zero product principle, $a\in\{4,10\}, $ ... both values satisfy (*). Solution set: $\{4,10\}$
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