Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations: 9

Answer

$x_{1}=\dfrac{2 + \sqrt{2}}{2}$ and $x_{2}=\dfrac{2 - \sqrt{2}}{2}$

Work Step by Step

Given $2x^2-4x+1=0 \\ $ $a=2, \ b=-4, \ c=1 \\ $ Therefore, using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} $ we have: $\dfrac{-(-4) \pm \sqrt{(-4)^2-4 \times 2 \times 1}}{2 \times 2} = \dfrac{4 \pm \sqrt{16-8}}{4} = \dfrac{4 \pm \sqrt{8}}{4} = \dfrac{4 \pm \sqrt{2^2 \times 2}}{4} = \dfrac{4 \pm 2\sqrt{2}}{4} = \dfrac{2 \pm \sqrt{2}}{2} \\ $ Therefore the solutions are $x_{1}=\dfrac{2 + \sqrt{2}}{2}$ and $x_{2}=\dfrac{2 - \sqrt{2}}{2}$
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