If a + b = 7 and ab = 10, find the value of a^2 + b^2.
Correct: A
We know the identity (a+b)^2 = a^2 + b^2 + 2ab.
We are given a + b = 7 and ab = 10.
Substitute these values into the identity:
(7)^2 = a^2 + b^2 + 2(10)
49 = a^2 + b^2 + 20
a^2 + b^2 = 49 - 20
a^2 + b^2 = 29.