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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.84 (page 316)

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

Short Answer

Expert verified

The value of x satisfying the equation is $x = - 4.236 a n d x = - 1.444$

Step by step solution

01

Given information

We are given a equation $\frac{e^{x} - e^{- x}}{2} = - 2$

02

Multiply both sides by ex and simplify

We get,

$e^{2 x} - 1 = - 4 e^{x} e^{2 x} + 4 e^{x} - 1 = 0$

03

Substitute ex=t and simplify

we get,

$t^{2} + 4 t - 1 = 0 t = \frac{- 4 卤 \sqrt{16 + 4}}{2} t = \frac{- 4 卤 2 \sqrt{5}}{2} t = - 2 卤 \sqrt{5} t = - 2 + \sqrt{5} o r t = - 2 - \sqrt{5}$

04

resubstitute

we get,

$e^{x} = - 2 - \sqrt{5} x = \ln (- 2 - \sqrt{5}) x = - 4.236 A n d e^{x} = - 2 + \sqrt{5} x = \ln (- 2 + \sqrt{5}) x = - 1.444$

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Most popular questions from this chapter

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