Question

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

Answer 1

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))`

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

Now plug the given value of xy=1

`=2^(4*1)`

`=2^(4)`

`=16`

Hence final answer is 16.