If xy = 1, what is the value of \small \frac{2^{(x+y)^{2}}}{2^{(x-y)^{2}}}

Question

asked Apr 5, 2019 60.7k views

1 Answer

Dmitry Birin · Answer 1 · 2019-04-11T02:26:09+0000

Given that xy=1. Now we have to use this equation to find the value of

(2^((x+y)^2))/(2^((x-y)^2))

$=2^(\left((x+y)^2-(x-y)^2\right))$

$=2^(\left(x^2+y^2+2xy-(x^2+y^2-2xy)\right))$

$=2^(\left(x^2+y^2+2xy-x^2-y^2+2xy\right))$

$=2^(\left(2xy+2xy\right))$

$=2^(\left(4xy\right))$

Now plug the given value of xy=1

=2^(4*1)

=2^(4)

=16

Hence final answer is 16.