Consider the following operators defined below
$x@y$: gives the positive difference of $x$ and $y.$
$x\$y$: gives the sum of squares of $x$ and $y.$
$x₤y$: gives the positive difference of the squares of $x$ and $y.$
$x\&y$:gives the product of $x$ and $y.$
Also, $x,y\:\in\:R\:\text{and}\:x\neq y$. The other standard algebraic operations are unchanged.
Given that $x@y=x-y$, then find $(x\$y)+(x₤y)$.
- $2x^2$
- $2y^2$
- $2(x^2+y^2)$
- Cannot be determined