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
(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