College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 64

Answer

$\displaystyle x=\frac{-1\pm\sqrt{17}}{8}$

Work Step by Step

$4+\displaystyle \frac{1}{x}-\frac{1}{x^{2}}=0$ We multiply by $x^2$: $x^{2}(4+\frac{1}{x}-\frac{1}{x^{2}})=x^{2}*0$ $4x^{2}+x-1=0$ We solve using the quadratic formula ($a=4,\ b=1,\ c=-1$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-1\pm\sqrt{1^{2}-4*4*-1}}{2*4}$ $\displaystyle x=\frac{-1\pm\sqrt{1+16}}{8}$ $\displaystyle x=\frac{-1\pm\sqrt{17}}{8}$
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