Use inspection to solve the equation x2=36/

Question

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. {−6/13,61/3} left brace negative Start Fraction 6 over 13 End Fraction comma 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}

Answer 1

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

Taking the square root of both sides gives:

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

This can be simplified as:

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

Therefore, 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 solution set is:

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