Question

If $a^2 + b^2 = 25$ and $ab = 12$, what is $(a + b)^2$?

• A. 37
• B. 49
• C. 61
• D. 73

Hint:

Use $(a + b)^2 = a^2 + b^2 + 2ab$ to find the sum of squares.

Answer 1

The Correct Option is B

- Step 1: Use identity: $(a + b)^2 = a^2 + b^2 + 2ab$.
- Step 2: Given $a^2 + b^2 = 25$, $ab = 12$.
- Step 3: Compute $2ab = 2 \times 12 = 24$.
- Step 4: So, $(a + b)^2 = 25 + 24 = 49$.
- Step 5: Verify: If $a + b = s$, then $s^2 - 2ab = a^2 + b^2 \implies s^2 = 25 + 24 = 49$.
- Step 6: Option (2) is 49, correct.