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Chisinau City MO
1976 Chisinau City MO
131
Chisinau MO p131 1976 X sum x_i^2 <= - nab if sum x_i=0
Chisinau MO p131 1976 X sum x_i^2 <= - nab if sum x_i=0
Source:
March 16, 2021
algebra
inequalities
Problem Statement
The sum of the real numbers
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ...,x_n
x
1
,
x
2
,
...
,
x
n
belonging to the segment
[
a
,
b
]
[a, b]
[
a
,
b
]
is equal to zero. Prove that
x
1
2
+
x
2
2
+
.
.
.
+
x
n
2
≤
−
n
a
b
.
x_1^2+ x_2^2+ ...+x_n^2 \le - nab.
x
1
2
+
x
2
2
+
...
+
x
n
2
≤
−
nab
.
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