Ask a New Question
Menu

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.

  1. Take the square root: \[ x = \pm \sqrt{\frac{36}{169}} \]

  2. Simplify the square root: \[ x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13} \]

Thus, the solutions are \( x = \frac{6}{13} \) and \( x = -\frac{6}{13} \).

Therefore, the correct solution set is: C. \({-\frac{6}{13}, \frac{6}{13}}\)