Use inspection to solve the equation x2=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.

{613}
left brace Start Fraction 6 over 13 End Fraction right brace

{−613}
left brace negative Start Fraction 6 over 13 End Fraction right brace

{−613,613}

1 answer

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

Taking the square root gives us:

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

Now, we can simplify the square root:

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

So, the solutions are:

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

Thus, the solution set is:

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

The correct response is:

{−6/13, 6/13}