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

To find \(a^2 + b^2\) given that \(a + b = 5\) and \(ab = 6\), we can use the identity:

\(a^2 + b^2 = (a+b)^2 - 2ab\)

1. Start by substituting the given values into the identity:
2. We know \(a + b = 5\) and \(ab = 6\).
3. Calculate \((a+b)^2\):
   • \((a+b)^2 = 5^2 = 25\)
4. Calculate \(2ab\):
   • \(2ab = 2 \times 6 = 12\)
5. Substitute these into the formula for \(a^2 + b^2\):
6. \(a^2 + b^2 = (a+b)^2 - 2ab = 25 - 12\)

Thus, \(a^2 + b^2 = 13\).

Therefore, the correct answer is 13.