If \(a-b=3\) and \(a^2+b^2=29\), find the value of ab.
Answer: A
We know the identity \((a-b)^2 = a^2+b^2-2ab\).
Substitute the given values into the identity:
\((3)^2 = 29 - 2ab\).
\(9 = 29 - 2ab\).
\(2ab = 29 - 9 = 20\).
\(ab = \frac{20}{2} = 10\).