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

$(x - y) = 3 - - - - (i)$

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

Adding equation (i) and (ii) we get
$2 x = 9$
$x = \frac{9}{2}$

Substituting the value of x in equation (ii) we get
$y = \frac{3}{2}$

$16 x^{2} y^{2} = 16 \times (\frac{9}{2})^{2} \times (\frac{3}{2})^{2} = 729$

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