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

$\frac{2^{(x+y)^2}}{2^{(x-y)^2}}$

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

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

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

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

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

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

Now plug the given value of xy=1

$=2^{4*1}$

$=2^{4}$

$=16$

Hence final answer is 16.