# How find the value of the x+yx+y

Question:

let $x,y\in \Bbb R$, and such

Find the $x+y$

This problem is from china some BBS

My idea: since

then I can’t Continue

Assuming the question is typed correctly as shown, there are two unique real solutions. Let These polynomials have exactly two distinct real roots; let $r(u,+)$, $r(u,-)$ be the positive and negative real roots of $u$, and $r(v,+)$, $r(v,-)$ be the positive and negative real roots of $v$, respectively. Then are the desired solutions. The sum $x+y$ can then be expressed by the solution to a third polynomial for which there are again two real roots, both positive. All of these polynomials are irreducible. So I highly doubt that this is a problem that can be reasonably solved by hand.