Question

Use inspection to solve the equation x^2 = 10^10, selecting the correct solutions set below.

{10^5}
{-5^5}
{-5^10,5^10}
{-10^5,10^5}

Answer 1

To solve the equation \( x^2 = 10^{10} \) using inspection, we can take the square root of both sides.

Taking the square root gives us:

\[
x = \pm 10^5
\]

This means that both \( 10^5 \) and \( -10^5 \) are solutions to the equation.

Now let's check the provided options:

1. \{10^5\} – This only includes the positive solution.
2. \{-5^5\} – This is incorrect because \( -5^5 = -3125 \) does not satisfy the equation.
3. \{-5^{10}, 5^{10}\} – This is incorrect because \( -5^{10} \) and \( 5^{10} = 10^{10} \) doesn't represent our solutions.
4. \{-10^5, 10^5\} – This correctly includes both solutions \( -10^5 \) and \( 10^5 \).

Thus, the correct solution set is:

\[
\{-10^5, 10^5\}
\]