Chapter 9: Q. 417 (page 1108)

In the following exercises, solve:
$\sqrt{4 v + 3} = \sqrt{v - 6}$ .

Short Answer

Expert verified

The solution is, $v = - 3$ .

Step by step solution

Step 1. Given Information.

The expression is,

$\sqrt{4 v + 3} = \sqrt{v - 6}$ .

Step 2. Finding the solution.

$\sqrt{4 v + 3} = \sqrt{v - 6}$

Squaring both sides,

role="math" localid="1647931083826" $\Rightarrow {(\sqrt{4 v + 3})}^{2} = {(\sqrt{v - 6})}^{2} \Rightarrow 4 v + 3 = v - 6$

Subtracting $3$ on both sides,

$\Rightarrow 4 v = v - 6 - 3 \Rightarrow 4 v = v - 9$

Subtracting $v$ both sides,

$\Rightarrow 4 v - v = - 9 \Rightarrow 3 v = - 9$

Dividing both sides by $3$ ,

$\Rightarrow \frac{3 v}{3} = \frac{- 9}{3} \Rightarrow v = - 3$

Step 3. Checking the solution.

$\sqrt{4 v + 3} = \sqrt{4 \times (- 3) + 3}$

$= \sqrt{- 12 + 3} = \sqrt{- 9}$

$\sqrt{v - 6} = \sqrt{- 3 - 6}$

$= \sqrt{- 9}$

The solution is true.

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In the following exercises, solve:
$\sqrt{4 v + 3} = \sqrt{v - 6}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

Step 3. Checking the solution.

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In the following exercises, solve:4v+3=v-6.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

Step 3. Checking the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve:
$\sqrt{4 v + 3} = \sqrt{v - 6}$ .