2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2

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Problem

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

Solution

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 $\boxed{x=-2+\sqrt[27]{2}}$

See also

2014 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All UNM-PNM Problems and Solutions
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