[/quote]
,
and 
, then we can deduce 
\le 2 $ ?
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)
be real numbers such that 
.
Let 
.
.![\[
0 \le (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \le 164.
\]](http://latex.artofproblemsolving.com/4/2/d/42d0b88388462f16dd99d928b94024e689ba7c2e.png)
and 
,
as follows:
where 
are all the positive divisors of 
.
Find all positive integers 
.
Find all positive integers 
.
be a convex quadrilateral. Suppose that the circles with diameters 
and 
intersect at points 
and 
.
and 
.
,
attaining all positive values and positive numbers 
are given. Numbers 
satisfy
for every 
.
.
?
and 
points on a plane is 
,
such that: in every set of 
points of a plane, no three of which are collinear, consisting of 
Y by
Given a convex quadrilateral whose opposite sides are not parallel, and giving an internal point 
. Find a parallelogram whose vertices are on the side lines of the rectangle and whose center is . Give a method by which we can construct it (provided there is one).
. Find a parallelogram whose vertices are on the side lines of the rectangle and whose center is . Give a method by which we can construct it (provided there is one).
This post has been edited 2 times. Last edited by parmenides51, Dec 15, 2020, 5:51 PM
