Intermediate Algebra (6th Edition)

Published by Pearson

Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set: 56

Answer

$m=\left\{ -6,0,6 \right\}$

Work Step by Step

The factored form of the given expression, $m^5=36m^3$, is \begin{array}{l} m^5-36m^3=0 \\\\ m^3(m^2-36)=0 \\\\ m^3(m+6)(m-6)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} m^3=0 \\ m=0 ,\text{ OR}\\\\ m+6=0 \\ m=0-6 \\ m=-6 ,\text{ OR}\\\\ m-6=0 \\ m=0+6 \\ m=6 \end{array} Hence, $m=\left\{ -6,0,6 \right\}$.

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