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

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== Solution == | == Solution == | ||

+ | We can write <math>f(x) = x^3 + 6x^2 + 12x + 6 = (x+2)^3 -2</math>. This means that <math>f(x) = 0 \Rightarrow x = \sqrt[3]{2} - 2</math>. | ||

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+ | Working backwards, <math>f(f(f(x))) = 0 \Rightarrow f(f(x)) = \sqrt[3]{2} - 2</math>. | ||

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+ | Then, <math>f(f(x)) = (f(x)-2)^3 - 2 = \sqrt[3]{2} - 2 \Rightarrow f(x) = \sqrt[9]{2}</math>. | ||

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+ | Finally, <math>f(x) = (x-2)^3 - 2 = \sqrt[9]{2} \Rightarrow \sqrt[3]{2+\sqrt[9]{2}}</math>. | ||

== See also == | == See also == |