Q. 422 In the following exercises, solv... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 422 (page 1108)

In the following exercises, solve.
$(a) \sqrt{u} + 1 = \sqrt{u + 4} (b) \sqrt{n - 5} + 4 = \sqrt{3 n + 7}$

Short Answer

Expert verified

Part (a) : The solutions for $\sqrt{u} + 1 = \sqrt{u + 4}$ is $\frac{9}{4}$

Part (b) : The solution for $\sqrt{n - 5} + 4 = \sqrt{3 n + 7}$ are 14 and 6

Step by step solution

Step 1. Given information

The given expressions are

$(a) \sqrt{u} + 1 = \sqrt{u + 4} (b) \sqrt{n - 5} + 4 = \sqrt{3 n + 7}$

Step 2. Squaring on both sides

$(a) \sqrt{u} + 1 = \sqrt{u + 4} {(\sqrt{u} + 1)}^{2} = {(\sqrt{u + 4})}^{2} u + 2 \sqrt{u} + 1 = u + 4 2 \sqrt{u} = 3 s q u a r i n g o n b o t h s i d e s 4 u = 9 u = \frac{9}{4}$

$(b) \sqrt{n - 5} + 4 = \sqrt{3 n + 7} s q u a r i n g o n b o t h s i d e s {(\sqrt{n - 5} + 4)}^{2} = {(\sqrt{3 n + 7})}^{2} {(\sqrt{n - 5})}^{2} + 4^{2} + 8 \sqrt{n - 5} = 3 n + 7 n - 5 + 16 + 8 \sqrt{n - 5} = 3 n + 7 8 \sqrt{n - 5} = 2 n - 4 A g a i n s q u a r i n g o n b o t h s i d e s {(8 \sqrt{n - 5})}^{2} = {(2 n - 4)}^{2} 64 (n - 5) = 4 n^{2} - 16 n + 16 64 n - 320 = 4 n^{2} - 16 n + 16 4 n^{2} - 80 n + 336 = 0 n = 14 n = 6$

The solutions are 14 and 6

Step 3. The solution

The solution for $\sqrt{u} + 1 = \sqrt{u + 4}$ is $\frac{9}{4}$

The solution for $\sqrt{n - 5} + 4 = \sqrt{3 n + 7}$ are 14 and 6

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91影视

In the following exercises, solve.
$(a) \sqrt{u} + 1 = \sqrt{u + 4} (b) \sqrt{n - 5} + 4 = \sqrt{3 n + 7}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Squaring on both sides

Step 3. The solution

One App. One Place for Learning.

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91影视

In the following exercises, solve.au+1=u+4bn-5+4=3n+7

Short Answer

Step by step solution

Step 1. Given information

Step 2. Squaring on both sides

Step 3. The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Probability and Statistics

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$(a) \sqrt{u} + 1 = \sqrt{u + 4} (b) \sqrt{n - 5} + 4 = \sqrt{3 n + 7}$