Use inspection to solve the equation x^2 = 36/169, then select the correct solution set below.

A. {6/13}
B. {-6/13}
C. {-6/13, 6/13}
D. There are no real solutions

1 answer

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

Starting with:

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

Taking the square root, we get:

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

Calculating the square root:

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

Thus, we have:

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

This gives us the solution set:

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

So, the correct solution set from the options provided is:

C. \({-6/13, 6/13}\)