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Poland - Second Round
2024 Poland - Second Round
5
Beautiful 6-variable inequality
Beautiful 6-variable inequality
Source: Polish MO Second round 2024 P5
February 10, 2024
inequalities
Problem Statement
The positive reals
a
,
b
,
c
,
x
,
y
,
z
a, b, c, x, y, z
a
,
b
,
c
,
x
,
y
,
z
satisfy
5
a
+
4
b
+
3
c
=
5
x
+
4
y
+
3
z
.
5a+4b+3c=5x+4y+3z.
5
a
+
4
b
+
3
c
=
5
x
+
4
y
+
3
z
.
Show that
a
5
x
4
+
b
4
y
3
+
c
3
z
2
≥
x
+
y
+
z
.
\frac{a^5}{x^4}+\frac{b^4}{y^3}+\frac{c^3}{z^2} \geq x+y+z.
x
4
a
5
+
y
3
b
4
+
z
2
c
3
≥
x
+
y
+
z
.
Proposed by Dominik Burek
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