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 $f(f(f(x))) = 0.$

Note that $f(x)=(x+2)^3-2$ . Thus $f(f(f(x)))=(x+2)^{27}-2$ . Setting this equal to zero and solving for $x$ , we have $\boxed{x=-2+\sqrt[27]{2}}$

2014 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All UNM-PNM Problems and Solutions