Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Mid-Chapter Check Point - Page 629: 10


$x = 2±2\sqrt{3}$

Work Step by Step

$\frac{1}{x^2}-\frac{4}{x}+1=0$ Multiply both sides by the least common multiple $x^2$ $\frac{1}{x^2}⋅x^2-\frac{4}{x}⋅x^2+1⋅x^2=0⋅x^2$ $1-4x+x^2=0$ Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$ $a=1$, $b=-4$, $c=1$ $x = \frac{-(-4)±\sqrt{(-4)^2-(4⋅1⋅1)}}{(2⋅1)}$ $x = \frac{4±\sqrt{12}}{2}$ $x = \frac{4±4\sqrt{3}}{2}$ $x = 2±2\sqrt{3}$
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