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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2017 India Regional Mathematical Olympiad
6
RMO 2017 P6
RMO 2017 P6
Source: RMO 2017 P6
October 8, 2017
inequalities
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be real numbers, each greater than
1
1
1
. Prove that
x
+
1
y
+
1
+
y
+
1
z
+
1
+
z
+
1
x
+
1
≤
x
−
1
y
−
1
+
y
−
1
z
−
1
+
z
−
1
x
−
1
\dfrac{x+1}{y+1}+\dfrac{y+1}{z+1}+\dfrac{z+1}{x+1} \leq \dfrac{x-1}{y-1}+\dfrac{y-1}{z-1}+\dfrac{z-1}{x-1}
y
+
1
x
+
1
+
z
+
1
y
+
1
+
x
+
1
z
+
1
≤
y
−
1
x
−
1
+
z
−
1
y
−
1
+
x
−
1
z
−
1
.
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