Math Olympiad Solution

[@user-ti8hk2wr9z]

i was thinking: sqrt(2+sqrt(x+2))=x
sqrt(2+sqrt(2+x))=x
this is the same as
sqrt(2+sqrt(2+sqrt(2+...)))
because you can infinitely recurse it
so x=sqrt(2+x)
x^2=2+x
x^2-x=2
x^2-x+1/4=8/4+1/4
(x-1/2)^2=9/4
x-1/2=±3/2
x=±3/2+1/2
however x

[@OlympiadSolutions]

That's also a nice approach