Question

Solve x2 = 78 by inspection. What are the two real solutions?(1 point) Responses {−74, 74 } {−74, 74 } {−72, 72 } {−72, 72 } {−78, 78 } {−78, 78 } {−74, 7−4 }

Answer 1

Pick one

Answer 2

To solve the equation \( x^2 = 78 \) by inspection, we need to find two real numbers whose square equals 78.

We know that:
- The square root of 78 is approximately 8.83 (since \( 8.83^2 \approx 78 \)).
- Thus, the two solutions can be \( \sqrt{78} \) and \( -\sqrt{78} \).

Since \( \sqrt{78} \approx 8.83 \), the two real solutions are approximately:
- \( x \approx 8.83 \)
- \( x \approx -8.83 \)

Looking at the provided options, none of them are exactly correct, as options like {-74, 74}, {-72, 72}, and {-78, 78} do not correspond to \( \sqrt{78} \) or \( -\sqrt{78} \).

However, the correct real solutions you are looking for in terms of the understanding of the problem are:
- \( \sqrt{78} \) and \( -\sqrt{78} \).

Thus, none of the provided answer choices are correct. If you are looking specifically for numerical values, you can estimate \( \sqrt{78} \) using the approximate values above.

Answer 3

Based on the equation \( x^2 = 78 \), the two real solutions are approximately \( \sqrt{78} \) and \( -\sqrt{78} \), which are roughly \( 8.83 \) and \( -8.83 \).

However, since none of the numerical answer choices provided match these solutions, the closest pair option that corresponds to having one positive and one negative solution would be:

**{−78, 78}**

This selection reflects the correct structure of one positive and one negative solution, even though the numerical values do not correspond to the square roots of 78. If you need to choose from the provided options, that's the best choice.