If $(2 x - 3 y) = 10$ and $x y = 8$ , find the value of $4 x^{2} + 9 y^{2}$

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100

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196

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Solution

The correct option is D
196

$(2 x - 3 y)^{2} = (10)^{2}$ [Squaring both sides]
$4 x^{2} + 9 y^{2} - 2 (2 x) (3 y) = 100$

$4 x^{2} + 9 y^{2} = 100 + 12 x y$
$= 100 + 12 (8) [∵ x y = 8]$
$= 100 + 96 = 196$

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