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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 168 (page 906)

In the following exercises, solve. ${(x^{2} - 4)}^{2} - 4 (x^{2} - 4) + 3 = 0$

Short Answer

Expert verified

Solution for equation will be

$x = + \sqrt{7}$
$x = - \sqrt{7}$
$x = + \sqrt{5}$
$x = - \sqrt{5}$

Step by step solution

01

Step 1. Given Data

Quadratic Equation is ${(x^{2} - 4)}^{2} - 4 (x^{2} - 4) + 3 = 0$

02

Step 2. To Find

We have to solve it and find the value of x.

03

Step 3. Explanation

Let the value of $(x^{2} - 4) = u$

Then the equation is -

${(x^{2} - 4)}^{2} - 4 (x^{2} - 4) + 3 = 0$

Put the value of $(x^{2} - 4) = u$

$u^{2} - 4 u + 3 = 0$

$(u - 3) (u - 1) = 0$

By using Zero product property -

$u - 3 = 0$ , $u - 1 = 0$

$u = 3$ , $u = 1$

04

Step 4. Calculation

Replace u with $(x^{2} - 4)$

$x^{2} - 4 = 3$ , $x^{2} - 4 = 1$

$x^{2} = 3 + 4$ , $x^{2} = 1 + 4$

$x^{2} = 7$ , $x^{2} = 5$

$x = 卤 \sqrt{7}$ , $x = 卤 \sqrt{5}$

There are four solutions -

$x = + \sqrt{7}$
$x = - \sqrt{7}$
$x = + \sqrt{5}$
$x = - \sqrt{5}$

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