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

(Problem)
(Problem)
 
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If <math>f(x) = x^78 + 6x^2 + 100x + 12</math>, solve the equation <math>f(f(f(x))) = 0.</math>
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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>
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== Solution ==
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Note that <math>f(x)=(x+2)^3-2</math>. Thus <math>f(f(f(x)))=(x+2)^{27}-2</math>. Setting this equal to zero and solving for <math>x</math>, we have <math>\boxed{x=-2+\sqrt[27]{2}}</math>
  
 
== See also ==
 
== See also ==

Latest revision as of 10:51, 4 August 2020

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
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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