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5
CNCM Online R1P5
CNCM Online R1P5
Source:
September 2, 2020
Problem Statement
Positive reals
a
,
b
,
c
≤
1
a,b,c \leq 1
a
,
b
,
c
≤
1
satisfy
a
+
b
+
c
−
a
b
c
1
−
a
b
−
b
c
−
c
a
=
1
\frac{a+b+c-abc}{1-ab-bc-ca} = 1
1
−
ab
−
b
c
−
c
a
a
+
b
+
c
−
ab
c
=
1
. Find the minimum value of
(
a
+
b
1
−
a
b
+
b
+
c
1
−
b
c
+
c
+
a
1
−
c
a
)
2
\bigg(\frac{a+b}{1-ab} + \frac{b+c}{1-bc} + \frac{c+a}{1-ca}\bigg)^{2}
(
1
−
ab
a
+
b
+
1
−
b
c
b
+
c
+
1
−
c
a
c
+
a
)
2
Proposed by Harry Chen (Extile)
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