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# Algebra

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

May 8, 2022

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We want 4x^2 + 9y^2, which is actually just (2x)^2 + (3y)^2, and the first equation looks kinda like it so we may try to expand the left-hand side of the first equation.

Using the identity (a - b)^2 = a^2 - 2ab + b^2,

$$\begin{array}{rcl} (2x - 3y)^2 &=& 4\\ (2x)^2 - 2(2x)(3y) + (3y)^2 &=& 4\\ 4x^2 - 12xy + 9y^2 &=& 4 \end{array}$$

We are almost there. The term we don't want is -12xy, but we know exactly what the value of -12xy is. Can you proceed from here?

May 8, 2022