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APMO
1998 APMO
3
Product of (1+a/b)
Product of (1+a/b)
Source: APMO 1998
March 17, 2006
inequalities
trigonometry
APMO
algebra
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be positive real numbers. Prove that
(
1
+
a
b
)
(
1
+
b
c
)
(
1
+
c
a
)
≥
2
(
1
+
a
+
b
+
c
a
b
c
3
)
.
\biggl(1+\frac{a}{b}\biggr) \biggl(1+\frac{b}{c}\biggr) \biggl(1+\frac{c}{a}\biggr) \ge 2 \biggl(1+\frac{a+b+c}{\sqrt[3]{abc}}\biggr).
(
1
+
b
a
)
(
1
+
c
b
)
(
1
+
a
c
)
≥
2
(
1
+
3
ab
c
a
+
b
+
c
)
.
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