Question

If $a + b = 5$ and $ab = 6$, find $a^2 + b^2$:

• A. 25
• B. 13
• C. 11
• D. 17

Hint:

You can also solve this by finding the numbers. Two numbers that add to 5 and multiply to 6 are 2 and 3. Then, $2^2 + 3^2 = 4 + 9 = 13$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem uses the algebraic identity: $(a + b)^2 = a^2 + b^2 + 2ab$.
Step 2: Detailed Explanation:
1. We know $(a + b)^2 = a^2 + b^2 + 2ab$. 2. Substitute the given values ($a+b=5$ and $ab=6$): $$(5)^2 = a^2 + b^2 + 2(6)$$ $$25 = a^2 + b^2 + 12$$ 3. Subtract 12 from both sides: $$a^2 + b^2 = 25 - 12 = 13$$
Step 3: Final Answer:
The correct option is (b).