To solve the equation \( x^2 = 36169 \) by inspection, we take the square root of both sides.
Calculating the square root:
\[ x = \sqrt{36169} \]
We can check if \( 36169 \) is a perfect square by finding its square root.
Calculating:
\[ \sqrt{36169} = 189 \]
So, \( x = 189 \) or \( x = -189 \) since both \( 189^2 \) and \( (-189)^2 \) equal \( 36169 \).
Thus the solution set is:
\[ { -189, 189 } \]
Since this specific set is not listed among your responses, please ensure that there was no misinterpretation of the original number \( 36169 \) and check if \( {-613, 613} \) might have been a typo or a different calculation. However, based on \( 36169 \), the choices available do not match.
Given the options:
- There are no real solutions.
- {−613}
- {613}
- {−613, 613}
None of these options correctly represents the results of our calculations.
The correct answer would be a solution set of \( { -189, 189 } \). If that isn't available, it might be due to an error in interpreting the number. Regarding your existing options, we conclude that there are valid real solutions, contradicting "There are no real solutions".
Since the response options do not include the correct values, none of them accurately reflects the solution. You could select "There are no real solutions" if required as a placeholder until further clarification can be obtained.
1 answer