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

 Mar 2, 2023
 #1
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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.

 Mar 2, 2023
 #2
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\((2x+3y)^{2}=4x^{2}+12xy+9y^{2}=4x^{2}-60+9y^{2}=4\)

\(4x^{2}+9y^{2}=64.\)

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 Mar 2, 2023

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