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239 Open Math Olympiad
2013 239 Open Mathematical Olympiad
8
5 variable inequality with product of 1
5 variable inequality with product of 1
Source: 239 2013 J8
August 7, 2020
algebra
inequalities
Problem Statement
The product of the positive numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
and
e
e
e
is equal to
1
1
1
. Prove that
a
2
b
2
+
b
2
c
2
+
c
2
d
2
+
d
2
e
2
+
e
2
a
2
≥
a
+
b
+
c
+
d
+
e
.
\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{d^2}+\frac{d^2}{e^2}+\frac{e^2}{a^2} \geq a+b+c+d+e .
b
2
a
2
+
c
2
b
2
+
d
2
c
2
+
e
2
d
2
+
a
2
e
2
≥
a
+
b
+
c
+
d
+
e
.
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