Question

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

Answer 1

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

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

We can simplify \( \sqrt{\frac{36}{169}} \):

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

Thus, the solutions are:

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

The solution set is:

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

Select the correct solution set:

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