Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 713: 43



Work Step by Step

Solving by setting the expressions equal to each other and then using the quadratic formula, we find: $$ \frac{3-x}{4}=\frac{1}{4x}\\ \left(3-x\right)\cdot \:4x=4\cdot \:1\\ -4x^2+12x-4=0\\ x_{1,\:2}=\frac{-12\pm \sqrt{12^2-4\left(-4\right)\left(-4\right)}}{2\left(-4\right)}\\ x=\frac{3-\sqrt{5}}{2},\:x=\frac{3+\sqrt{5}}{2}$$
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