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All-Russian Olympiad
1979 All Soviet Union Mathematical Olympiad
278
ASU 278 All Soviet Union MO 1979 (x_1 +...+ x_n + 1)^2 \ge 4(x_1^2 +...+ x_n^2)
ASU 278 All Soviet Union MO 1979 (x_1 +...+ x_n + 1)^2 \ge 4(x_1^2 +...+ x_n^2)
Source:
July 14, 2019
algebra
inequalities
Problem Statement
Prove that for the arbitrary numbers
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ... , x_n
x
1
,
x
2
,
...
,
x
n
from the
[
0
,
1
]
[0,1]
[
0
,
1
]
segment
(
x
1
+
x
2
+
.
.
.
+
x
n
+
1
)
2
≥
4
(
x
1
2
+
x
2
2
+
.
.
.
+
x
n
2
)
(x_1 + x_2 + ...+ x_n + 1)^2 \ge 4(x_1^2 + x_2^2 + ... + x_n^2)
(
x
1
+
x
2
+
...
+
x
n
+
1
)
2
≥
4
(
x
1
2
+
x
2
2
+
...
+
x
n
2
)
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