If x + 2y= 4 and xy = -8, what is the value of x^2 + 4y^2?

x + 2y = 4 square both sides

(x + 2y)^2 = 16

x^2 + 4xy + 4y^2 = 16 [xy = -8 ]

x^2 + 4(-8) + 4y^2 = 16

x^2 + 4y^2 - 32 = 16

x^2 + 4y^2 = 48