College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 139: 46

Answer

$x=\frac{-3-\sqrt{17}}{2}$

Work Step by Step

$\sqrt {3-x}+2=1-x$ $3-x=x^2+2x+1$ $x^2+2x+1=3-x$ $x^2+3x-2=0$ By quadratic formula: $x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}$ $x_{1,\:2}=\frac{-3\pm \sqrt{17}}{2}$ Test: $x=\frac{-3+\sqrt{17}}{2}$ $\sqrt {3-x}+2=1-x$ $\sqrt {3-\frac{-3+\sqrt{17}}{2}}+2=1-\frac{-3+\sqrt{17}}{2}$ $\:3.56155\ne 0.43844 $ Test: $x=\frac{-3-\sqrt{17}}{2}$ $\sqrt {3-x}+2=1-x$ $\sqrt {3-\frac{-3-\sqrt{17}}{2}}+2=1-\frac{-3-\sqrt{17}}{2}$ $4.56155= \:4.56155 $
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