Question

Use inspection to solve the equation x2=1010
, selecting the correct solution set below. (1 point)
Responses

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

{105}

left brace 10 superscript 5 baseline right brace

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

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

Answer 1

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

Taking the square root of both sides, we have:

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

Now, we can estimate \( \sqrt{1010} \). We know that:

\[
\sqrt{1000} \approx 31.62
\]

Since \( 1010 \) is slightly greater than \( 1000 \), we can deduce that \( \sqrt{1010} \) is slightly greater than \( 31.62 \).

Comparing \( 32^2 \) and \( 31^2 \):

\[
31^2 = 961 \quad \text{and} \quad 32^2 = 1024
\]

Since \( 1010 \) is between \( 961 \) and \( 1024 \), we find that \( \sqrt{1010} \) is between \( 31 \) and \( 32 \).

From this, we can deduce that the approximate values for \( x \) would be around \( \pm 31.62 \). Let's look for matching options:

1. \( \{ -510, 510 \} \) – Not correct as they are way off.
2. \( \{ 10^5 \} \) – This equals \( 100,000 \), not correct.
3. \( \{ -55 \} \) – Not correct since \( (-55)^2 = 3025 \).
4. \( \{ -10^5, 10^5 \} \) – Again, this is clearly off.

None of these choices seem to suggest the correct approximate roots of \( \pm \sqrt{1010} \), which are roughly \( \pm 31.62 \).

It appears that there might be confusion in expressing the options—likely they intended \( \{ -\sqrt{1010}, \sqrt{1010} \} \) in some form.

But based on what is provided, there is no option that correctly represents \( \sqrt{1010} \) or \( -\sqrt{1010} \). If I had to select the response closest or more reasonable, I would suggest noting that none of the options is correct for solving \( x^2 = 1010 \).