Chapter 9: Q. 419 (page 1108)

In the following exercises, solve:
$\sqrt{12 c + 6} = \sqrt{10 - 4 c}$ .

Short Answer

Expert verified

The solution is, $c = \frac{1}{4}$ .

Step by step solution

Step 1. Given Information.

The expression is,

$\sqrt{12 c + 6} = \sqrt{10 - 4 c}$ .

Step 2. Finding the solution.

$\sqrt{12 c + 6} = \sqrt{10 - 4 c}$

Squaring both sides,

role="math" localid="1647933105428" $\Rightarrow {(\sqrt{12 c + 6})}^{2} = {(\sqrt{10 - 4 c})}^{2} \Rightarrow 12 c + 6 = 10 - 4 c$

Subtracting $6$ from both sides,

$\Rightarrow 12 c = 10 - 4 c - 6 \Rightarrow 12 c = - 4 c + 4$

Adding $4 c$ on both sides,

$\Rightarrow 12 c + 4 c = 4 \Rightarrow 16 c = 4$

Dividing both sides by role="math" localid="1647933260020" $16$ ,

role="math" localid="1647933248751" $\Rightarrow \frac{16 c}{16} = \frac{4}{16} \Rightarrow c = \frac{1}{4}$

Step 3. Checking the solution.

$\sqrt{12 c + 6} = \sqrt{12 \times \frac{1}{4} + 6}$

$= \sqrt{3 + 6} = \sqrt{9}$

$\sqrt{10 - 4 c} = \sqrt{10 - 4 \times \frac{1}{4}}$

$= \sqrt{10 - 1} = \sqrt{9}$

The solution is true.

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In the following exercises, solve:
$\sqrt{12 c + 6} = \sqrt{10 - 4 c}$ .

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:12c+6=10-4c.

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

Logic and Functions

Discrete Mathematics

Applied Mathematics

Calculus

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve:
$\sqrt{12 c + 6} = \sqrt{10 - 4 c}$ .