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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 329 (page 824)

In the following exercises, solve.
$\sqrt[3]{2 x^{2} + 9 x - 18} = \sqrt[3]{x^{2} + 3 x - 2}$

Short Answer

Expert verified

The solutions of the given equation are $x = - 8$ and $x = 2$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt[3]{2 x^{2} + 9 x - 18} = \sqrt[3]{x^{2} + 3 x - 2}$

02

Step 2. Simplify the equation.

Take cube on both sides.

$\begin{array}{rcl} (\sqrt[3]{2 x^{2} + 9 x - 18})^{3} & = & (\sqrt[3]{x^{2} + 3 x - 2})^{3} \\ 2 x^{2} + 9 x - 18 & = & x^{2} + 3 x - 2 \\ 2 x^{2} + 9 x - 18 - x^{2} - 3 x + 2 & = & 0 \\ x^{2} + 6 x - 16 & = & 0 \end{array}$

03

Step 3. Solve the equation.

Splitting the middle term, the above equation can be written as:

\begin{array}{rcl} x^{2} + 8 x - 2 x - 16 & = & 0 \\ x (x + 8) - 2 (x + 8) & = & 0 \\ (x + 8) (x - 2) & = & 0 \\ x & = & - 8, 2 \end{array}

04

Step 4. Conclusion.

The solutions of the given equation are $x = - 8$ and $x = 2$ .

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