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An easy problem from silk road 2016
Source: silk road mathematical olympiad 2016,P1
4/4/2016
Let
a
,
b
a,b
a
,
b
and
c
c
c
be real numbers such that
∣
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
∣
=
1
| (a-b) (b-c) (c-a) | = 1
∣
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
∣
=
1
. Find the smallest value of the expression
∣
a
∣
+
∣
b
∣
+
∣
c
∣
| a | + | b | + | c |
∣
a
∣
+
∣
b
∣
+
∣
c
∣
. (K.Satylhanov )
algebra
inequalities proposed
inequalities