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1971 IMO Shortlist
17
Prove the fractional inequality - ISL 1971
Prove the fractional inequality - ISL 1971
Source:
September 22, 2010
Inequality
4-variable inequality
four variables
IMO Shortlist
Problem Statement
Prove the inequality
a
1
+
a
3
a
1
+
a
2
+
a
2
+
a
4
a
2
+
a
3
+
a
3
+
a
1
a
3
+
a
4
+
a
4
+
a
2
a
4
+
a
1
≥
4
,
\frac{a_1+ a_3}{a_1 + a_2} + \frac{a_2 + a_4}{a_2 + a_3} + \frac{a_3 + a_1}{a_3 + a_4} + \frac{a_4 + a_2}{a_4 + a_1} \geq 4,
a
1
+
a
2
a
1
+
a
3
+
a
2
+
a
3
a
2
+
a
4
+
a
3
+
a
4
a
3
+
a
1
+
a
4
+
a
1
a
4
+
a
2
≥
4
,
where
a
i
>
0
,
i
=
1
,
2
,
3
,
4.
a_i > 0, i = 1, 2, 3, 4.
a
i
>
0
,
i
=
1
,
2
,
3
,
4.
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