If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2.

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

Options:

A . 27

B . 81

C . 243

D . 729

Answer: Option D
:
D

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

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

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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