Question

Solve the following equation.
$\sqrt[4]{41+5x}+\sqrt[4]{45-y}=3,5x-y=11$.

Answer 1

$x=0,y=-11$ or $x=3,y=4$
Hint: Put $\sqrt[4]{41+5x}=u$ and $\sqrt[4]{45-y}=v$. Then
$u+v=3,u^4+v^4=17$
Solving these symmetric equations, we shall get
$u=1,v=2$ or $u=2,v=1$ etc