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If 2x +3y = 8 and xy = 2, find the value of 4x^2 + 9y^2

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If 2x + 3y = 8 and xy = 2, find the value of 4x2 + 9y2

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Here, we will use (a+b)2 = a2 + b2 + 2ab

Given: 2x + 3y = 8 and xy = 2

We write, (2x + 3y)2 = (2x)2 + (3y)2 + 2 x 2x x 3y

(8)2 = 4x2 + 9y2 + 12xy

64 = 4x2 + 9y2 + 24

4x2 + 9y2 = 64 - 24 = 40

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