Use inspection to solve the equation x2=1010

Question

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

{−105,105}
left brace negative 10 superscript 5 baseline comma 10 superscript 5 baseline right brace

{−55}
left brace negative 5 superscript 5 baseline right brace

{−510,510}
left brace negative 5 superscript 10 baseline comma 5 superscript 10 baseline right brace

{105}

Answer 1

To solve the equation \( x^2 = 1010 \) using inspection, we need to find the values of \( x \) such that when squared, they equal 1010.

Calculating the square root of 1010:

\[ x = \pm \sqrt{1010} \]

Since \( \sqrt{1010} \) is not a perfect square, we can approximate its value. The approximate value is:

\[ \sqrt{1010} \approx 31.78 \]

Thus, the possible solutions for \( x \) are approximately:

\[ x \approx 31.78 \quad \text{and} \quad x \approx -31.78 \]

Now, if we look at the options provided:

1. {−105, 105}
2. {−55}
3. {−510, 510}
4. {105}

None of these values are approximately \( 31.78 \) or \( -31.78 \). However, it seems that there may have been a misunderstanding with the formatting of the options. If the closest option based on the calculated values were available, we would select an approximate set that includes both positive and negative values for a square root.

Given the mathematical steps, the answer that fits best with our calculations would be:

\[ \text{The correct solution set based on the options provided is neither of the options given, but it should include: } {-31.78, 31.78} \]

However, from the provided options, none directly correspond. The answer is closest to the form that includes both positive and negative values of an approximate square root, which is closest represented by:

{−105, 105}

(Note: This depends on the available choices; none align perfectly with the calculated value.)