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If $(2x + 3y)^2 = 4$ and $xy = -5$, what is the value of $4x^2 + 9y^2$?

Guest Mar 2, 2023

Guest · Answer 1 · 2023-03-02T04:03:33

Solving the system (2x + 3y)^2 = 4 and xy = -5, we get x = -(sqrt(14) + 1)/2 and y = (sqrt(14) - 1)/3.

Then 4x^2 + 9y^2 = 4*(-(sqrt(14) + 1)/2)^2 + 9((sqrt(14) - 1)/3)^2 = 30.

Guest · Answer 2 · 2023-03-02T05:23:52

$(2x+3y)^{2}=4x^{2}+12xy+9y^{2}=4x^{2}-60+9y^{2}=4$

$4x^{2}+9y^{2}=64.$

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