# Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2"

## Problem

If $f(x) = x^3 + 6x^2 + 12x + 6$, solve the equation $f(f(f(x))) = 0.$

## Solution 2

Note that $f(x)=(x+2)^3-2$. Thus, $f^{n}(x)=(x+2)^{3n}-2$. In the question, $n=3$, so we have $(x+2)^{27}-2=0$. Solving, $\boxed{x=-2+\sqrt[27]{2}}$

~yofro