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

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

Guest May 1, 2021

CPhill · Answer 1 · 2021-05-01T09:44:21

x + 2y = 4

xy = -8

Square both sides of the the first equation

x^2 + 4xy + 4y^2 = 16

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

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

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

x^2 + 4y^2 = 48