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National and Regional Contests
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All-Russian Olympiad
1973 All Soviet Union Mathematical Olympiad
187
ASU 187 All Soviet Union MO 1973 (Σx_i)^2 \ge 4(x_1x_2+x_3x_4+x_5x_1+..)
ASU 187 All Soviet Union MO 1973 (Σx_i)^2 \ge 4(x_1x_2+x_3x_4+x_5x_1+..)
Source:
July 4, 2019
inequalities
algebra
Problem Statement
Prove that for every positive
x
1
,
x
2
,
x
3
,
x
4
,
x
5
x_1, x_2, x_3, x_4, x_5
x
1
,
x
2
,
x
3
,
x
4
,
x
5
holds inequality:
(
x
1
+
x
2
+
x
3
+
x
4
+
x
5
)
2
≥
4
(
x
1
x
2
+
x
3
x
4
+
x
5
x
1
+
x
2
x
3
+
x
4
x
5
)
(x_1 + x_2 + x_3 + x_4 + x_5)^2 \ge 4(x_1x_2 + x_3x_4 + x_5x_1 + x_2x_3 + x_4x_5)
(
x
1
+
x
2
+
x
3
+
x
4
+
x
5
)
2
≥
4
(
x
1
x
2
+
x
3
x
4
+
x
5
x
1
+
x
2
x
3
+
x
4
x
5
)
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