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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q.81 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\frac{e^{x} + e^{- x}}{2} = 1$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 0$ .

Step by step solution

01

Given information

We are given an equation $\frac{e^{x} + e^{- x}}{2} = 1$

02

Simplify

multiply both sides by $e^{x}$

we get,

$e^{2 x} + 1 = 2 e^{x} e^{2 x} - 2 e^{x} + 1 = 0$

03

Substitute ex=t and solve for t

We get,

$t^{2} - 2 t + 1 = 0 {(t - 1)}^{2} = 0 t = 1$

04

Solve for x

We get

$e^{x} = t e^{x} = 1 e^{x} = e^{0} 鈭� x = 0$

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