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International Contests
Tournament Of Towns
1989 Tournament Of Towns
(213) 1
TOT 213 1989 Spring Train S1 a^2 + 3b^2 + 5c^2 + 7 d^2 >= 1
TOT 213 1989 Spring Train S1 a^2 + 3b^2 + 5c^2 + 7 d^2 >= 1
Source:
March 7, 2021
algebra
inequalities
Problem Statement
The positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
satisfy
a
≤
b
≤
c
≤
d
a\le b\le c\le d
a
≤
b
≤
c
≤
d
and
a
+
b
+
c
+
d
≤
1
a + b + c + d \le 1
a
+
b
+
c
+
d
≤
1
. Prove that
a
2
+
3
b
2
+
5
c
2
+
7
d
2
≥
1
a^2 + 3b^2 + 5c^2 + 7 d^2 \ge 1
a
2
+
3
b
2
+
5
c
2
+
7
d
2
≥
1
.
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