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Azerbaijan Junior National Olympiad
2016 Azerbaijan Junior Mathematical Olympiad
6
Inequality.
Inequality.
Source:
February 7, 2016
Inequality
algebra
inequalities
Azerbaijan
Problem Statement
For all reals
x
,
y
,
z
x,y,z
x
,
y
,
z
prove that
x
2
+
1
y
2
+
y
2
+
1
z
2
+
z
2
+
1
x
2
≥
3
2
.
\sqrt {x^2+\frac {1}{y^2}}+ \sqrt {y^2+\frac {1}{z^2}}+ \sqrt {z^2+\frac {1}{x^2}}\geq 3\sqrt {2}.
x
2
+
y
2
1
+
y
2
+
z
2
1
+
z
2
+
x
2
1
≥
3
2
.
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