Question

Use inspection to solve the equation x^2=36/169 , then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)
Responses

{−6/13,6/13}
left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace

{6/13}
left brace Start Fraction 6 over 13 End Fraction right brace

There are no real solutions.
There are no real solutions.

{−6/13}

Answer 1

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

\[
x = \pm \sqrt{\frac{36}{169}}
\]

Calculating the square root gives us:

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

This results in two solutions:

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

Thus, the solution set is:

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

The correct response is:

\(\{-\frac{6}{13}, \frac{6}{13}\}\)