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International Contests
Tournament Of Towns
1989 Tournament Of Towns
(203) 1
TOT 203 1989 Spring Train J1 a^2 + 3b^2 + 5c^2 <= 1
TOT 203 1989 Spring Train J1 a^2 + 3b^2 + 5c^2 <= 1
Source:
March 7, 2021
algebra
inequalities
Problem Statement
The positive numbers
a
,
b
a, b
a
,
b
and
c
c
c
satisfy
a
≥
b
≥
c
a \ge b \ge c
a
≥
b
≥
c
and
a
+
b
+
c
≤
1
a + b + c \le 1
a
+
b
+
c
≤
1
. Prove that
a
2
+
3
b
2
+
5
c
2
≤
1
a^2 + 3b^2 + 5c^2 \le 1
a
2
+
3
b
2
+
5
c
2
≤
1
. (F . L . Nazarov)
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