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A5
ab + bc + ca = 18
ab + bc + ca = 18
Source: Junior Olympiad of Malaysia Shortlist 2015 A5
July 17, 2015
Inequality
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the side length of a triangle, with
a
b
+
b
c
+
c
a
=
18
ab + bc + ca = 18
ab
+
b
c
+
c
a
=
18
and
a
,
b
,
c
>
1
a, b, c > 1
a
,
b
,
c
>
1
. Prove that
∑
c
y
c
1
(
a
−
1
)
3
>
1
a
+
b
+
c
−
3
\sum_{cyc}\frac{1}{(a - 1)^3} > \frac{1}{a + b + c - 3}
cyc
∑
(
a
−
1
)
3
1
>
a
+
b
+
c
−
3
1
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