be positive real numbers satisfying 
.![\[
3(x^{\frac{2}{3}} + y^{\frac{2}{3}}) \geq 4 + 2x^{\frac{1}{3}}y^{\frac{1}{3}}.
\]](http://latex.artofproblemsolving.com/f/3/c/f3cd114f909f388eacee142d3f90d07f6b149131.png)
with another positive integer 
,
is a perfect square. For example, if the number on the blackboard is 
,
,
,
,
.
,
and 
,
to be the unique polynomial 
such that we can write 
,
is a polynomial such that either 
or the degree of 
with real coefficients such that 
be non-negative real numbers such that 
Prove that
Y by
Let 
be a circle with center 
and diameter 
, and 
the midpoint of an arc . extends beyond 
to a point 
. 
is a point such that 
and the line 
passes through the midpoint 
of 
. Let 
be the point of tangency from to in the arc that does not contain . The intersections of 
with 
and 
with 
are 
and 
respectively. Show that 
and 
are parallel.
be a circle with center 
and diameter 
, and 
the midpoint of an arc . extends beyond 
to a point 
. 
is a point such that 
and the line 
passes through the midpoint 
of 
. Let 
be the point of tangency from to in the arc that does not contain . The intersections of 
with 
and 
with 
are 
and 
respectively. Show that 
and 
are parallel.This post has been edited 2 times. Last edited by parmenides51, Sep 8, 2021, 4:07 AM
