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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. 158 (page 906)

In the following exercises, solve. $x^{4} + 5 x^{2} - 36 = 0$

Short Answer

Expert verified

Solution for equation will be

$x = + 2$
$x = - 2$
$x = + \sqrt{(- 9)}$
$x = - \sqrt{(- 9)}$

Step by step solution

01

Step 1. Given Data

Quadratic Equation is $x^{4} + 5 x^{2} - 36 = 0$

02

Step 2. To Find

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

03

Step 3. Explanation

Let the value of $x^{2} = u$

Then the equation is -

$x^{4} + 5 x^{2} - 36 = 0$

${(x^{2})}^{2} + 5 x^{2} - 36 = 0$

Put the value of $x^{2} = u$

$u^{2} + 5 u - 36 = 0$

$(u - 4) (u + 9) = 0$

By using Zero product property -

$u - 4 = 0$ , $u + 9 = 0$

$u = 4$ , $u = (- 9)$

04

Step 4. Calculation

Replace u with $x^{2}$

$x^{2} = 4$ , $x^{2} = (- 9)$

Using the square root property -

$x = 卤 \sqrt{4}$ , $x = 卤 \sqrt{(- 9)}$

$x = 卤 2$ , $x = 卤 \sqrt{(- 9)}$

There are four solutions -

$x = + 2$
$x = - 2$
$x = + \sqrt{(- 9)}$
$x = - \sqrt{(- 9)}$

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