Prove that
be positive real numbers. Prove 
.![\[
\sum_{\text{cyc}} \frac{x^3}{y^2 + z^2} \geq \frac{x + y + z}{2}
\]](http://latex.artofproblemsolving.com/9/0/3/903220c471bdd3028dda2fcb13874a4bcf752872.png)
without using the Rearrangement Inequality or Chebyshev's Inequality.
,
.
.
, where 
always occurs at 
such that 
divides 
.
such that:
for all 
.
and 
are real numbers such that
If a problem has not been solved within 
days, then others are eligible to post a new probkem.
,
)
and 
If each person remains there for 
minutes, what's the probability that all three people meet each other?
and solve for the area of a hexagon in that 
square.
is an arithmetic sequence, 
,
.
of the sequence 
be 
,
be the sum of the 
.
Y by Mango247
A set 
of points in the 
-dimensional space is called interesting, if for any plane there exist at least 
points in outside this plane. For which minimal 
any interesting set contains an interesting subset with at most points?
(IMC 2013.9)
of points in the 
-dimensional space is called interesting, if for any plane there exist at least 
points in outside this plane. For which minimal 
any interesting set contains an interesting subset with at most points?(IMC 2013.9)
This post has been edited 1 time. Last edited by parmenides51, Mar 15, 2021, 9:29 PM
