Chapter 5: Q.83 (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 values of x which satisfies the given equation is $x = - 0.236 a n d x = 1.444$

Step by step solution

Given information

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

multiply both sides by ex

we get,

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

Substitute ex=t and solve for t

We get,

$t^{2} - 4 t - 1 = 0 t = \frac{4 \pm \sqrt{16 + 4}}{2} t = \frac{4 \pm \sqrt{20}}{2} t = \frac{4 \pm 2 \sqrt{5}}{2} t = 2 \pm \sqrt{5}$

Now again substitute

we get

$e^{x} = t e^{x} = 2 - \sqrt{5} x = - 0.236 A n d e^{x} = 2 + \sqrt{5} x = 1.444$

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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

Substitute ex=t and solve for t

Now again substitute

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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

Substitute ex=t and solve for t

Now again substitute

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Geometry

Applied Mathematics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

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