Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 706: 160


There is no real solution.

Work Step by Step

Solve the provided equation, $\begin{align} & 2\cos x-1+3\sec x=0 \\ & 2\operatorname{cosx}+3\frac{1}{\cos x}=1 \\ & \frac{2{{\cos }^{2}}x+3}{\cos x}=1 \\ & 2{{\cos }^{2}}x+3-\cos x=0 \end{align}$ And use the quadratic formula, $\cos x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ $\begin{align} & 2{{\cos }^{2}}x-\cos x+3=0 \\ & \cos x=\frac{1\pm \sqrt{1-4\left( 2 \right)\left( 3 \right)}}{2\left( 2 \right)} \\ & \cos x=\frac{1\pm \sqrt{-11}}{4} \end{align}$ Thus, there is no real solution for the provided equation.
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