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

Revision as of 01:15, 4 August 2020

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

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 If <math>f(x) = x^3 + 6x^2 + 12x + 6</math>, solve the equation <math>f(f(f(x))) = 0.</math>
-==Solution 2==
-Note that <math>f(x)=(x+2)^3-2</math>. Thus, <math>f^{n}(x)=(x+2)^{3n}-2</math>. In the question, <math>n=3</math>, so we have <math>(x+2)^{27}-2=0</math>. Solving, <math>\boxed{x=-2+\sqrt[27]{2}}</math>
-~yofro
 == See also ==

2014 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNM-PNM Problems and Solutions