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

Given information

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

Multiply both sides by ex and simplify

We get,

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

Substitute ex=t and simplify

we get,

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

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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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

Step by step solution

Given information

Multiply both sides by ex and simplify

Substitute ex=t and simplify

resubstitute

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:ex-e-x2=-2

Short Answer

Step by step solution

Given information

Multiply both sides by ex and simplify

Substitute ex=t and simplify

resubstitute

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Applied Mathematics

Calculus

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

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