Algebra 1

Published by Prentice Hall

Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 617: 40

Answer

$x=6-4\sqrt{2}\approx0.3$

Work Step by Step

Rationalize the left side's denominator first by multiplying by its conjugate. $\frac{\sqrt{2}-1}{\sqrt{2}+1}\cdot \frac{\sqrt{2}-1}{\sqrt{2}-1}=\frac{x}{2}=\frac{2-2\sqrt{2}+1}{2-1}=3-2\sqrt{2}. x=6-4\sqrt{2}\approx0.3$

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