Question:
If $x^2 + y^2 = 25$ and $xy = 12$, what is $x + y$?
If $x^2 + y^2 = 25$ and $xy = 12$, what is $x + y$?
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When $x^2+y^2$ and $xy$ are known, use $(x+y)^2 = x^2 + y^2 + 2xy$ to find $x+y$ directly.
Updated On: Aug 1, 2025
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The Correct Option is B
Solution and Explanation
- Step 1: Recall algebraic identity - \[ (x+y)^2 = x^2 + y^2 + 2xy \]
- Step 2: Substitute known values - Given $x^2 + y^2 = 25$, $xy = 12$: \[ (x+y)^2 = 25 + 2 \times 12 = 25 + 24 = 49 \]
- Step 3: Take square root - \[ x+y = \pm \sqrt{49} = \pm 7 \]
- Step 4: Choose sign based on context - Usually, if no restriction is given, we take the positive root: $x + y = 7$.
- Step 5: Conclusion - $x + y = 7$, matching option (2).
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