MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2006 Korea National Olympiad
6
6
Part of
2006 Korea National Olympiad
Problems
(1)
3-Vari Ineq
Source: 2006 Korea National Olympid #6
3/18/2018
Prove that for any positive real numbers
x
,
y
x,y
x
,
y
and
z
,
z,
z
,
x
y
z
(
x
+
2
)
(
y
+
2
)
(
z
+
2
)
≤
(
1
+
2
(
x
y
+
y
z
+
z
x
)
3
)
3
xyz(x+2)(y+2)(z+2)\le(1+\frac{2(xy+yz+zx)}{3})^3
x
yz
(
x
+
2
)
(
y
+
2
)
(
z
+
2
)
≤
(
1
+
3
2
(
x
y
+
yz
+
z
x
)
)
3
inequalities
algebra