If x - y = 4 and xy = 21, find the value of x^2 + y^2.
Correct: C
We know the identity (x-y)^2 = x^2 + y^2 - 2xy.
We are given x - y = 4 and xy = 21.
Substitute these values into the identity:
(4)^2 = x^2 + y^2 - 2(21)
16 = x^2 + y^2 - 42
x^2 + y^2 = 16 + 42
x^2 + y^2 = 58.