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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2007 Korea Junior Math Olympiad
5
5
Part of
2007 Korea Junior Math Olympiad
Problems
(1)
\frac{a}{c+5b}+\frac{b}{a+5c}+\frac{c}{b+5a}\geq\frac{1}{2} , for a,b,c>0
Source: KJMO 2007 p5
5/2/2019
For all positive real numbers
a
,
b
,
c
.
a, b,c.
a
,
b
,
c
.
Prove the folllowing inequality
a
c
+
5
b
+
b
a
+
5
c
+
c
b
+
5
a
≥
1
2
.
\frac{a}{c+5b}+\frac{b}{a+5c}+\frac{c}{b+5a}\geq\frac{1}{2}.
c
+
5
b
a
+
a
+
5
c
b
+
b
+
5
a
c
≥
2
1
.
algebra
inequalities
Inequality
three variable inequality