If $2 x + 3 y = 8 a n d x y = 2, f i n d t h e v a l u e o f 4 x^{2} + 9 y^{2} .$

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Solution

$2 x + 3 y = 8 a n d x y = 2$

Now, $(2 x + 3 y)^{2} = (2 x)^{2} + (3 y)^{2} + 2 \times 2 x \times 3 y \Rightarrow (8)^{2} = 4 x^{2} + 9 y^{2} + 12 x y \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 12 \times 2 \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 24 \Rightarrow 4 x^{2} + 9 y^{2} = 64 - 24 = 40 ∴ 4 x^{2} + 9 y^{2} = 40$

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