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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 416 (page 1108)

In the following exercises, solve:
$\sqrt{3 u - 2} = \sqrt{5 u + 1}$ .

Short Answer

Expert verified

The solution is, $u = - \frac{3}{2}$ .

Step by step solution

01

Step 1. Given Information.

The expression is,

$\sqrt{3 u - 2} = \sqrt{5 u + 1}$ .

02

Step 2. Finding the solution.

$\sqrt{3 u - 2} = \sqrt{5 u + 1}$

Squaring both sides,

role="math" localid="1647890790168" $鈬� {(\sqrt{3 u - 2})}^{2} = {(\sqrt{5 u + 1})}^{2} 鈬� 3 u - 2 = 5 u + 1$

Adding $2$ on both sides,

$鈬� 3 u = 5 u + 1 + 2 鈬� 3 u = 5 u + 3$

Subtracting $5 u$ on both sides,

$鈬� 3 u - 5 u = 3 鈬� - 2 u = 3$

Dividing both sides by $(- 2)$ ,

$鈬� \frac{- 2 u}{- 2} = \frac{3}{- 2} 鈬� u = - \frac{3}{2}$

03

Step 3. Checking the solution.

$\sqrt{3 u - 2}$

Inputting $u = - \frac{3}{2}$ ,

$= \sqrt{3 脳 (- \frac{3}{2}) - 2} = \sqrt{- \frac{9}{2} - 2} = \sqrt{\frac{- 9 - 4}{2}} = \sqrt{- \frac{13}{2}}$

$\sqrt{5 u + 1}$

Inputting $u = - \frac{3}{2}$ ,

$= \sqrt{5 脳 (- \frac{3}{2}) + 1} = \sqrt{- \frac{15}{2} + 1} = \sqrt{\frac{- 15 + 2}{2}} = \sqrt{- \frac{13}{2}}$

The solution is true.

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