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1
Find the value of a^2b+b^2c+c^2a
Find the value of a^2b+b^2c+c^2a
Source: Swiss Imo Selection 2006
May 25, 2006
invariant
function
algebra proposed
algebra
Problem Statement
The three roots of
P
(
x
)
=
x
3
−
2
x
2
−
x
+
1
P(x) = x^3 - 2x^2 - x + 1
P
(
x
)
=
x
3
−
2
x
2
−
x
+
1
are
a
>
b
>
c
∈
R
a>b>c \in \mathbb{R}
a
>
b
>
c
∈
R
. Find the value of
a
2
b
+
b
2
c
+
c
2
a
a^2b+b^2c+c^2a
a
2
b
+
b
2
c
+
c
2
a
. :D
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