Question
Use inspection to solve the equation x2=1010
, selecting the correct solution set below. (1 point)
Responses
{−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
{−510,510}
left brace negative 5 superscript 10 baseline comma 5 superscript 10 baseline right brace
{105}
, selecting the correct solution set below. (1 point)
Responses
{−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
{−510,510}
left brace negative 5 superscript 10 baseline comma 5 superscript 10 baseline right brace
{105}
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( x^2 = 1010 \), we need to find the values of \( x \) that satisfy this equation.
Taking the square root of both sides gives us:
\[
x = \pm \sqrt{1010}
\]
Now we need to approximate \( \sqrt{1010} \). Since \( 31^2 = 961 \) and \( 32^2 = 1024 \), we can infer that:
\[
31 < \sqrt{1010} < 32
\]
Calculating it more precisely, \( \sqrt{1010} \) is approximately \( 31.78 \). Thus, we get the approximate values:
\[
x \approx 31.78 \quad \text{and} \quad x \approx -31.78
\]
Neither of the possible solutions is a perfect square or round number. Among the given options, the set of solutions that includes both positive and negative roots around this approximation is:
\(\{-32, 32\}\) or similar options, but since none are exactly approximate and looking closely:
The closest matching correct solution appears to be {−105, 105} since it represents both negative and positive values.
However, to be strictly correct regarding true roots:
The roots would be more accurately related to numbers around 31.78 or quite closer to 32.
Since none of the options correctly represent \( \sqrt{1010} \), considering expectations, look, we guided:
The answer chosen in context from provided should lead you to finalize:
\{−105, 105\} as reflected selection adhering towards point wise under considerations.
If specifying closely to results, then {±32} would have ideally suffice which may somewhat mislead all ends bound to formats available.
Taking the square root of both sides gives us:
\[
x = \pm \sqrt{1010}
\]
Now we need to approximate \( \sqrt{1010} \). Since \( 31^2 = 961 \) and \( 32^2 = 1024 \), we can infer that:
\[
31 < \sqrt{1010} < 32
\]
Calculating it more precisely, \( \sqrt{1010} \) is approximately \( 31.78 \). Thus, we get the approximate values:
\[
x \approx 31.78 \quad \text{and} \quad x \approx -31.78
\]
Neither of the possible solutions is a perfect square or round number. Among the given options, the set of solutions that includes both positive and negative roots around this approximation is:
\(\{-32, 32\}\) or similar options, but since none are exactly approximate and looking closely:
The closest matching correct solution appears to be {−105, 105} since it represents both negative and positive values.
However, to be strictly correct regarding true roots:
The roots would be more accurately related to numbers around 31.78 or quite closer to 32.
Since none of the options correctly represent \( \sqrt{1010} \), considering expectations, look, we guided:
The answer chosen in context from provided should lead you to finalize:
\{−105, 105\} as reflected selection adhering towards point wise under considerations.
If specifying closely to results, then {±32} would have ideally suffice which may somewhat mislead all ends bound to formats available.
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