Use inspection to solve the equation x2=10^10

Question

, selecting the correct solution set below. (1 point)
Responses

{−105,105}
start set negative 10 to the 5th power comma 10 to the 5th power end set - no response given

{−55}
start set negative 5 to the 5th power end set - no response given

{−510,510}
start set negative 5 to the 10th power comma 5 to the 10th power end set - no response given

{105}

Answer 1

To solve the equation \(x^2 = 10^{10}\) by inspection, we first recognize that taking the square root of both sides gives us:

\[ x = \pm \sqrt{10^{10}} \]

We can simplify \(\sqrt{10^{10}}\):

\[ \sqrt{10^{10}} = 10^{10/2} = 10^5 = 100000 \]

Therefore, the solutions are:

\[ x = 10^5 \quad \text{and} \quad x = -10^5 \]

This results in the solution set:

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

In numerical form, this is:

\[ {-100000, 100000} \]

Now, comparing with the given options, the correct solution set from your provided responses is:

\({-10^5, 10^5}\) which corresponds to:

\({-105, 105}\) (though it's written slightly differently, it conveys the same numerical values).

So, the correct answer is:

\({-10^5, 10^5}\) (or {-105, 105} as interpreted).