Chapter 10: Q26. (page 629)

Solve each equation. Check your solution.
$\sqrt{3 x^{2} - 32} = x$

Short Answer

Expert verified

The solution of the given equation is $x = 4$ .

Step by step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$\sqrt{3 x^{2} - 32} = x {(\sqrt{3 x^{2} - 32})}^{2} = x^{2} (squaringbothsides) 3 x^{2} - 32 = x^{2}$

Step 2. Solve the given equation.

The solution of the given equation is:

$3 x^{2} - 32 = x^{2} 3 x^{2} - x^{2} = 32 2 x^{2} = 32 x^{2} = 16 x = \pm \sqrt{16} x = \pm \sqrt{4^{2}} x = \pm 4$

Therefore, the values of x are $x = 4$ or $x = - 4$ .

Step 3. Check the solutions.

Check the solution $x = 4$ ,

Substitute 4 for x in the given equation $\sqrt{3 x^{2} - 32} = x$ .

$\sqrt{3 x^{2} - 32} = x \sqrt{3 {(4)}^{2} - 32} \underline{\underline{?}} 4 \sqrt{48 - 32} \underline{\underline{?}} 4 \sqrt{16} \underline{\underline{?}} 4 4 = 4$

Therefore, $x = 4$ is the solution of the given equation $\sqrt{3 x^{2} - 32} = x$ .

Check the solution $x = - 4$ ,

Substitute $- 4$ for x in the given equation width="101" height="26" role="math">3x2−32=x.

$\sqrt{3 x^{2} - 32} = x \sqrt{3 {(- 4)}^{2} - 32} \underline{\underline{?}} - 4 \sqrt{48 - 32} \underline{\underline{?}} - 4 \sqrt{16} \underline{\underline{?}} - 4 4 \neq - 4$

Therefore, $x = - 4$ is not the solution of the given equation $\sqrt{3 x^{2} - 32} = x$ .

Therefore, the only solution of the given equation $\sqrt{3 x^{2} - 32} = x$ is $x = 4$ .

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Solve each equation. Check your solution.
$\sqrt{3 x^{2} - 32} = x$

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solutions.

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Solve each equation. Check your solution.3x2−32=x

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Decision Maths

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution.
$\sqrt{3 x^{2} - 32} = x$