Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapter 9 Test - Page 431: 24



Work Step by Step

Squaring both sides of the equation and using the properties of radicals, the solution to the given equation is \begin{array}{l}\require{cancel}\left( \sqrt{n-3} \right)^2=\left( 3-n \right)^2 \\\\ n-3=(3)^2+2(3)(-n)+(-n)^2 \\\\ n-3=9-6n+n^2 \\\\ 0=(9+3)+(-6n-n)+n^2 \\\\ 12-7n+n^2=0 \\\\ (4-n)(3-n)=0 \\\\ n=\{3,4\} .\end{array} Upon checking, only $ n=3 $ satisfies the original equation.
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