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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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

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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

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Study anywhere. Anytime. Across all devices.

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