Define a sequence of functions f₀, f₁, f₂, ......, by

f₀(x)= 8, for all real x, and
f_n+1(x) = sqrt(x² + 6f_n(x)); for all real x and all non-negative integers n.

Solve the equation

f_n(x)= 2x

(In reply to Solution? by tomarken)

Clearly x=4 is a solution as you have said.  The implied question would then seem to be "Is x=4 the only solution for each n?"

Posted by Richard on 2006-11-19 12:01:06