be a monic polynomial with integer coefficient. And suppose there exist 4 distinct integer 
such that 
.
such that 
such that ![\[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]](http://latex.artofproblemsolving.com/0/6/2/0623b7c328af6d088cfc5dd288afe3e17a94ff29.png)
for all reals 
and 
.
sastifying 
Y by Adventure10, Mango247
A point 
is given inside a triangle 
. Let 
be the midpoints of 
, and let 
be the intersection points of 
and 
and 
and 
, respectively.
(a) Prove that the area of hexagon
is equal to one third of the area of triangle .
(b) Prove that
, and 
are concurrent.
is given inside a triangle 
. Let 
be the midpoints of 
, and let 
be the intersection points of 
and 
and 
and 
, respectively.(a) Prove that the area of hexagon
is equal to one third of the area of triangle .(b) Prove that
, and 
are concurrent.This post has been edited 1 time. Last edited by parmenides51, Jul 28, 2018, 10:24 AM
Reason: latex
Reason: latex
