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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 714 (page 1151)

In the following exercises, solve the equation:
$\sqrt{r} + 3 = \sqrt{r + 4}$

Short Answer

Expert verified

The required value of the given equation has no solution.

Step by step solution

01

Step 1. Given information

Given expression is $\sqrt{r} + 3 = \sqrt{r + 4}$

02

Step 2. Solve the equation using square roots.

$\sqrt{r} + 3 = \sqrt{r + 4} 鈬� r + 6 \sqrt{r} + 9 = r + 4 鈬� 6 \sqrt{r} + 9 = 4 鈬� 6 \sqrt{r} = 4 - 9 鈬� 6 \sqrt{r} = - 5 鈬� \sqrt{r} = - \frac{5}{6} 鈬� {(\sqrt{r})}^{2} = {(- \frac{5}{6})}^{2} 鈬� r = \frac{25}{36}$

03

Step 3. Check

L.H.S

$\sqrt{r} + 3 = \sqrt{\frac{25}{36}} + 3 = \frac{5}{6} + 3 = \frac{23}{6}$

R.H.S

$\sqrt{r + 4} = \sqrt{\frac{25}{36} + 4} = \sqrt{\frac{25 + 144}{36}} = \sqrt{\frac{169}{36}} = \frac{13}{6}$

Left hand side is not equal to right hand side.

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