Question

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

• A. 5
• B. 7
• C. 9
• D. 11

Hint:

Use $(x + y)^2 = x^2 + y^2 + 2xy$ to find the sum when $x^2 + y^2$ and $xy$ are given.

Answer 1

The Correct Option is B

- Step 1: Given $x^2 + y^2 = 25$ and $xy = 12$. Find $x + y$.
- Step 2: Use identity: $(x + y)^2 = x^2 + y^2 + 2xy$.
- Step 3: Substitute: $(x + y)^2 = 25 + 2 \times 12 = 49$, so $x + y = \pm \sqrt{49} = \pm 7$.
- Step 4: Since options are positive, take $x + y = 7$.
- Step 5: Verify: If $x + y = 7$, then $x^2 + y^2 + 2xy = 49$. Given $xy = 12$, so $x^2 + y^2 = 49 - 24 = 25$, which matches.
- Step 6: Check options: Option (b) is 7, which matches.