Easiest one!!!

Applying AM $\ge$ GM as $x,\ y>0$ and positive,

$\frac{x+y}{2}\ge\sqrt{xy}$

$\implies\frac{x+y}{2}\ge 1\ \ \ \because xy=1$

$\implies x+y\ge 2$

Minimum value of $x+y$ is $2$

x,y is greater than 1.so only positive number which can give result 1 is (1multiplied by 1).

so 1+1=2.

A product will achieve the minimum sum of two factors if these two factors are equal to each other. In the case of all positive numbers, this can be achieved with two equal positive or two equal negative factors. However, because this problem specifies that $x,y>0$ , we only need to find the sum of two equal positive factors. In the case of $1$ , these factors are $1$ and $1$ , and $1+1=\boxed{2}$ .

This would be a great trick question if it weren't specified that $x,y>0$ .

The only value of x and y is 1 because their product should be 1. 1 + 1 = 2