Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set: 22

Answer

$y=\{ 0,49 \}$

Work Step by Step

Squaring both sides of the given equation, $ 7\sqrt{y}=y ,$ results to \begin{array}{l}\require{cancel} 7\sqrt{y}=y \\\\ \left( 7\sqrt{y} \right)^2=(y)^2 \\\\ 49y=y^2 \\\\ 0=y^2-49y \\\\ y^2-49y=0 .\end{array} Factoring the $GCF=y,$ the equation above is equivalent to \begin{array}{l}\require{cancel} y^2-49y=0 \\\\ y(y-49)=0 .\end{array} Equating each factor to zero (Zero Product Property), the solutions are \begin{array}{l}\require{cancel} y=0 \\\\\text{OR}\\\\ y-49=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} y=0 \\\\\text{OR}\\\\ y-49=0 \\\\ y=49 .\end{array} Upon checking, both solutions satisfy the original equation. Hence, $ y=\{ 0,49 \} .$
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