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

Latest revision as of 20:51, 17 January 2021

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

Revision as of 11:51, 4 August 2020 (view source) Yofro (talk \| contribs) (→‎Problem) ← Older edit		Latest revision as of 20:51, 17 January 2021 (view source) Gavin6152 (talk \| contribs) (→‎Problem)
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−	If <math>f(x) = x^2+6x^2+12x+6</math>, solve the equation <math>f(f(f(x))) = 0.</math>	+	If <math>f(x) = x^3+6x^2+12x+6</math>, solve the equation <math>f(f(f(x))) = 0.</math>

	== Solution ==		== Solution ==

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