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

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Solution

Given
$2 x + 3 y = 8$ and $x y = 2$ ,

formula,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$∴ (2 x + 3 y)^{2} = 4 x^{2} + 9 y^{2} + 2 (2 x) (3 y)$

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

$8^{2} = 4 x^{2} + 9 y^{2} + 12 (2)$

$∴ 4 x^{2} + 9 y^{2} = 64 - 24 = 40$

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$I f 2 x + 3 y = 14 a n d 2 x - 3 y = 2, find the value of xy.$

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4 x^{2} + 9 y^{2}

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