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Inequality with a+b+c=1 - Fractional Inequality
Inequality with a+b+c=1 - Fractional Inequality
Source:
November 3, 2010
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive numbers with the sum
1
1
1
. Prove the inequality
1
1
−
a
+
1
1
−
b
+
1
1
−
c
≥
2
1
+
a
+
2
1
+
b
+
2
1
+
c
.
\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c} \geq \frac{2}{1+a}+\frac{2}{1+b}+\frac{2}{1+c}.
1
−
a
1
+
1
−
b
1
+
1
−
c
1
≥
1
+
a
2
+
1
+
b
2
+
1
+
c
2
.
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