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

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

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

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

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

Answer 1

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

First, we rewrite the equation:

\[
x^2 = \frac{36}{169}
\]

Taking the square root of both sides, we have:

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

We can simplify this:

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

Thus, the solutions are:

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

Therefore, the correct solution set is:

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

So the correct response is:

{−6/13, 6/13}