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1998 Korea Junior Math Olympiad
6
(1998 KJMO P6) inequality on a/b+b/c+c/a
(1998 KJMO P6) inequality on a/b+b/c+c/a
Source: 1998 KJMO P6
June 30, 2024
inequalities
KJMO
Problem Statement
For positive reals
a
≥
b
≥
c
≥
0
a \geq b \geq c \geq 0
a
≥
b
≥
c
≥
0
prove the following inequality:
a
b
+
b
c
+
c
a
≥
a
+
b
a
+
c
+
b
+
c
b
+
a
+
c
+
a
c
+
b
\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{a+b}{a+c}+\frac{b+c}{b+a}+\frac{c+a}{c+b}
b
a
+
c
b
+
a
c
≥
a
+
c
a
+
b
+
b
+
a
b
+
c
+
c
+
b
c
+
a
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