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Akdeniz University MO
1998 Akdeniz University MO
3
Inequality (easy)
Inequality (easy)
Source: A book
January 30, 2016
inequalities
easy inequality
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be non-negative numbers such that
x
+
y
+
z
≤
3
x+y+z \leq 3
x
+
y
+
z
≤
3
. Prove that
2
1
+
x
+
2
1
+
y
+
2
1
+
z
≥
3
\frac{2}{1+x}+\frac{2}{1+y}+\frac{2}{1+z} \geq 3
1
+
x
2
+
1
+
y
2
+
1
+
z
2
≥
3
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