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2011 JBMO Shortlist
2
&Sigma;(x + 2y)(z + 2x + 3y) <= 3/2
&Sigma;(x + 2y)(z + 2x + 3y) <= 3/2
Source: JBMO 2011 Shortlist A2
October 14, 2017
JBMO
algebra
inequalities
Problem Statement
Let
x
,
y
,
z
x, y, z
x
,
y
,
z
be positive real numbers. Prove that:
x
+
2
y
z
+
2
x
+
3
y
+
y
+
2
z
x
+
2
y
+
3
z
+
z
+
2
x
y
+
2
z
+
3
x
≤
3
2
\frac{x + 2y}{z + 2x + 3y}+\frac{y + 2z}{x + 2y + 3z}+\frac{z + 2x}{y + 2z + 3x} \le \frac{3}{2}
z
+
2
x
+
3
y
x
+
2
y
+
x
+
2
y
+
3
z
y
+
2
z
+
y
+
2
z
+
3
x
z
+
2
x
≤
2
3
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