Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 64

Answer

$\{3\}$

Work Step by Step

Step 1. Given the equation $\sqrt {3\sqrt {2x+3}}=\sqrt {5x-6}$ Step 2. Take square on both sides to get: $3\sqrt {2x+3}=5x-6$ Step 3. Take square on both sides again to get: $18x+27=25x^2-60x+36$ or $25x^2-78x+9=0$ which gives $x=\frac{3}{25},3$ Step 4. Check answers in the original equation: only $\{3\}$ fits.
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