MathDB
Problems
Contests
National and Regional Contests
Thailand Contests
Thailand National Olympiad
2023 Thailand Mathematical Olympiad
6
Easy a,b,c,x,y IE
Easy a,b,c,x,y IE
Source: 2023 Thailand MO Day 2 P6
May 12, 2023
inequalities
Problem Statement
Let
a
,
b
,
c
,
x
,
y
a,b,c,x,y
a
,
b
,
c
,
x
,
y
be positive real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. Prove that
a
5
x
c
+
y
b
+
b
5
x
a
+
y
c
+
c
5
x
b
+
y
a
≥
9
(
x
+
y
)
(
a
2
+
b
2
+
c
2
)
.
\frac{a^5}{xc+yb}+\frac{b^5}{xa+yc}+\frac{c^5}{xb+ya}\geq \frac{9}{(x+y)(a^2+b^2+c^2)}.
x
c
+
y
b
a
5
+
x
a
+
yc
b
5
+
x
b
+
y
a
c
5
≥
(
x
+
y
)
(
a
2
+
b
2
+
c
2
)
9
.
Back to Problems
View on AoPS