Question

Use inspection to solve the equation $x^{2}=\frac {36}{169}$ then select the correct solution set below. If there
are no real solutions , select"There are no real solutions." (1 point)
$\{ -\frac {6}{13}\} $
$\{ -\frac {6}{13},\frac {6}{13}\} $
There are no real solutions
$\{ \frac {6}{13}\} $

Answer 1

To solve the equation \( x^2 = \frac{36}{169} \) using inspection, we will take the square root of both sides.

First, we recognize that taking the square root of both sides yields two potential solutions:

\[
x = \sqrt{\frac{36}{169}} \quad \text{or} \quad x = -\sqrt{\frac{36}{169}}.
\]

Calculating the square root on the right side, we have:

\[
\sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13}.
\]

Thus, the two possible solutions for \( x \) are:

\[
x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13}.
\]

This gives us the complete solution set:

\[
\{ -\frac{6}{13}, \frac{6}{13} \}.
\]

Now, referring to the options provided, the correct solution set is:

\[
\{ -\frac{6}{13}, \frac{6}{13} \}.
\]