If x + y = 7 and xy = 10, find the value of x^2 + y^2.
(A) 23
(B) 49
(C) 29
(D) 61
Answer: (C) 29
Solution:
Squaring both sides of the equation x + y = 7,
we get x^2 + 2xy + y^2 = 49.
Substituting xy = 10,
we get x^2 + 2 * 10 + y^2 = 49.
Solving for x^2 + y^2,
we get x^2 + y^2 = 49 – 20 = 29.
=> x^2 + y^2 = 29
