Question

Solve x2=78 by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses. (1 point) Write it as basiccally as possible
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Answer 1

how would i write that, like -78^2, 78^2?

Answer 2

To solve the equation \( x^2 = 78 \) by inspection, we recognize that \( x \) can take both positive and negative values.

1. The positive solution is \( x = \sqrt{78} \).
2. The negative solution is \( x = -\sqrt{78} \).

Since \( \sqrt{78} \) is approximately \( 8.83 \), the two real solutions are \( -\sqrt{78} \) and \( \sqrt{78} \).

Thus, the solutions can be entered as:
\[
\{-\sqrt{78}, \sqrt{78}\}
\]

Answer 3

To write the solutions in the requested format using exponents, you would represent the square roots in terms of exponents as follows:

- The negative solution can be written as \( -78^{1/2} \).
- The positive solution can be written as \( 78^{1/2} \).

Therefore, the two solutions in the format you specified would be:

\[
\{-78^{1/2}, 78^{1/2}\}
\]