Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2: 51

Answer

The solution set is $\left\{-11, 11\right\}$.

Work Step by Step

The given equation can be written as: $n^2-11^2=0$ RECALL: A difference of two squares can be factored using the formula: $a^2-b^2=(a-b)(a+b)$ Factor the difference of two squares to obtain: $(n-11)(n+11)=0$ Equate each factor to 0, and then solve each equation to obtain: $n-11=0 \text{ or } n+11 = 0 \\n=11 \text{ or } n=-11$ The solution set is $\left\{-11, 11\right\}$.
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