If $(x^{2} - y^{2}) = 18$ and $(x - y) = 3$ , find the value of $16 x^{2} y^{2}$ .

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243

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729

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Solution

The correct option is D
729

Given, $(x^{2} - y^{2}) = (x - y) (x + y) = 18$

Also, $(x - y) = 3$ ------------ (1)

$\Rightarrow (x + y) = \frac{18}{3} = 6$ ------------ (2)

Solving equations (1) and (2), we get $x = \frac{9}{2}$ and $y = \frac{3}{2}$
$\Rightarrow 16 x^{2} y^{2} = 16 \times (\frac{9}{2})^{2} \times (\frac{3}{2})^{2} = 729$

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