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All-Russian Olympiad
1987 All Soviet Union Mathematical Olympiad
452
ASU 452 All Soviet Union MO 1987 a+A=b+B=c+C=k => aB+bC+cA <=k^2
ASU 452 All Soviet Union MO 1987 a+A=b+B=c+C=k => aB+bC+cA <=k^2
Source:
August 7, 2019
algebra
inequalities
Problem Statement
The positive numbers
a
,
b
,
c
,
A
,
B
,
C
a,b,c,A,B,C
a
,
b
,
c
,
A
,
B
,
C
satisfy a condition
a
+
A
=
b
+
B
=
c
+
C
=
k
a + A = b + B = c + C = k
a
+
A
=
b
+
B
=
c
+
C
=
k
Prove that
a
B
+
b
C
+
c
A
≤
k
2
aB + bC + cA \le k^2
a
B
+
b
C
+
c
A
≤
k
2
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