Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 60

Answer

$y=\{ -5,-4\}$

Work Step by Step

Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation is \begin{array}{l}\require{cancel}\left( \sqrt{y+5} \right)^2=\left( y+5 \right)^2 \\\\ y+5=(y)^2+2(y)(5)+(5)^2 \\\\ y+5=y^2+10y+25 \\\\ 0=y^2+(10y-y)+(25-5) \\\\ y^2+9y+20=0 \\\\ (y+4)(y+5)=0 \\\\ y=\{ -5,-4\} .\end{array} Upon checking, both solutions, $ y=\{ -5,-4\} ,$ satisfy the original equation.
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