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239 Open Math Olympiad
2008 239 Open Mathematical Olympiad
2
1/a + 1/b + 1/c = 1 Inequality
1/a + 1/b + 1/c = 1 Inequality
Source: 239 2008 J2
July 28, 2020
inequalities
algebra
Problem Statement
For all positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfying
1
a
+
1
b
+
1
c
=
1
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1
a
1
+
b
1
+
c
1
=
1
, prove that:
a
a
+
b
c
+
b
b
+
c
a
+
c
c
+
a
b
≥
3
4
.
\frac{a}{a+bc} + \frac{b}{b+ca} + \frac{c}{c+ab} \geq \frac{3}{4} .
a
+
b
c
a
+
b
+
c
a
b
+
c
+
ab
c
≥
4
3
.
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