Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.7 - Polynomial and Rational Inequalities - Exercise Set - Page 413: 26

Answer

$[1-\sqrt 3,1+\sqrt 3]$

Work Step by Step

Step 1. Rewrite the inequality as $x^2-2x-2\leq0$ or $(x-(1-\sqrt 3))(x-(1+\sqrt 3))\leq0$ and the boundary points are $x=1\pm\sqrt 3$ Step 2. Using test points to examine signs across the boundary points, we have $...(+)...(1-\sqrt 3)...(-)...(1+\sqrt 3)...(+)...$ Thus the solutions are $1-\sqrt 3\leq x\leq 1+\sqrt 3$ Step 3. We can express the solutions on a real number line as shown in the figure. Step 4. We can express the solutions in interval notation as $[1-\sqrt 3,1+\sqrt 3]$
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