MathDB
Problems
Contests
National and Regional Contests
China Contests
XES Mathematics Olympiad
the 11th XMO
2
2
Part of
the 11th XMO
Problems
(1)
Hard 3 variable inequality
Source:
2/9/2023
Suppose
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
and
a
b
c
=
64
abc=64
ab
c
=
64
, show that
∑
c
y
c
a
2
a
3
+
8
b
3
+
8
≥
2
3
\sum_{cyc}\frac{a^2}{\sqrt{a^3+8}\sqrt{b^3+8}}\ge\frac{2}{3}
cyc
∑
a
3
+
8
b
3
+
8
a
2
≥
3
2
algebraic inequality
inequalities