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1
a, b, c are integers greater than 1
a, b, c are integers greater than 1
Source: Romanian MO 2010 Grade 8
August 6, 2012
inequalities proposed
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be integers larger than
1
1
1
. Prove that
a
(
a
−
1
)
+
b
(
b
−
1
)
+
c
(
c
−
1
)
≤
(
a
+
b
+
c
−
4
)
(
a
+
b
+
c
−
5
)
+
4.
a(a-1)+b(b-1)+c(c-1)\le (a+b+c-4)(a+b+c-5)+4.
a
(
a
−
1
)
+
b
(
b
−
1
)
+
c
(
c
−
1
)
≤
(
a
+
b
+
c
−
4
)
(
a
+
b
+
c
−
5
)
+
4.
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