If x + y = 5 and xy = 6, find the value of x^2 + y^2.

If x + y = 5 and xy = 6, find the value of x^2 + y^2.

(A) 11

(B) 25

(C) 13

(D) 36

Answer: (C) 13

Solution:

(x + y)^2 = x^2 + 2xy + y^2

5^2 = x^2 + 2(6) + y^2

25 = x^2 + 12 + y^2

x^2 + y^2 = 25 – 12

x^2 + y^2 = 13