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Baltic Way
2019 Baltic Way
1
Asymmetric Inequality
Asymmetric Inequality
Source: 2019 Baltic Way P1
November 18, 2019
algebra
inequalities
Problem Statement
For all non-negative real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
with
x
≥
y
x \geq y
x
≥
y
, prove the inequality
x
3
−
y
3
+
z
3
+
1
6
≥
(
x
−
y
)
x
y
z
.
\frac{x^3-y^3+z^3+1}{6}\geq (x-y)\sqrt{xyz}.
6
x
3
−
y
3
+
z
3
+
1
≥
(
x
−
y
)
x
yz
.
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