Talk:2007 AIME II Problems/Problem 14
Revision as of 23:52, 15 August 2021 by Wzs26843545602 (talk | contribs)
Here is a completed solution to 2007AIMEII-14.
Let .
.
.
or
(impossible).
Let
.
Then
and the same thing got:$\[f_1 \left( x \right) \equiv 1]$ (Error compiling LaTeX. Unknown error_msg) or
.
Let
be an integer and $\[f_n \left( x \right) = \frac{{f\left( x \right)}}{{\left( {x^2 + 1} \right)^n }}$ such that$ (Error compiling LaTeX. Unknown error_msg)\[deg f_n \left( x \right) = 0{\text{ or }}1$.Then $\[f_n \left( x \right) = 1{\rm{ or }}x + 1]$.Check if$ (Error compiling LaTeX. Unknown error_msg)f\left( 2 \right) + f\left( 3 \right) = 125
n = 2
f_n \left( x \right) = 1
f\left( 5 \right) = \boxed{625}$.