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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 602 (page 857)

In the following exercises, solve.
$\sqrt[3]{2 x^{2} - 6 x - 23} = \sqrt[3]{x^{2} - 3 x + 5}$

Short Answer

Expert verified

The solution of the equation is $x = 7, - 4$

Step by step solution

01

Step 1. Given Information

We have $\sqrt[3]{2 x^{2} - 6 x - 23} = \sqrt[3]{x^{2} - 3 x + 5}$

02

Step 2. Cubing both sides

${(\sqrt[3]{2 x^{2} - 6 x - 23})}^{3} = {(\sqrt[3]{x^{2} - 3 x + 5})}^{3} 2 x^{2} - 6 x - 23 = x^{2} - 3 x + 5$

$x^{2} - 3 x - 28 = 0$

03

Step 3. Factorize the expression

$x^{2} - 3 x - 28 = 0 (x - 7) (x + 4) = 0 x = 7, - 4$

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Most popular questions from this chapter

Explain what is meant by the $n^{t h}$ root of a number.

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{96}$

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[3]{625}$ , b. $\sqrt[6]{128}$

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