Question

If $x^2 + y^2 = 25$ and $xy = 12$, what is $x + y$? 
 

• A. 5
• B. 7
• C. 9
• D. 11

Hint:

When $x^2+y^2$ and $xy$ are known, use $(x+y)^2 = x^2 + y^2 + 2xy$ to find $x+y$ directly.

Answer 1

The Correct Option is B

- 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).