Infinite square root muliplication $(x=3\sqrt{y\sqrt{3\sqrt{y}....}})$ I have this problem which says
$$
x=3\sqrt{y\sqrt{3\sqrt{y\cdots}}}\\
y=3\sqrt{x\sqrt{3\sqrt{x\cdots}}}
$$
What is $x+y$
I tried 
$$
x^2=9y\sqrt{x}\\
x^3=81y^2\\
y^3=81x^2\\
x^3+y^3=81(x^2+y^2)\\
(x+y)(x^2-xy+y^2)=81(x^2+y^2)
$$
I don't know what to do or if I am do that right 

From second equality we obtain
$$x^2=9x\sqrt{x},$$ which gives $x=0$ or $x=81$. The rest is smooth. 
