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Greece Contests
Greece National Olympiad
2002 Greece National Olympiad
1
1
Part of
2002 Greece National Olympiad
Problems
(1)
Inequality
Source: Greece National Olympiad 2002 , Seniors , Problem 1.
11/18/2005
The real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
b
c
≠
0
bc\neq0
b
c
=
0
satisfy
1
−
c
2
b
c
≥
0.
\frac{1-c^2}{bc}\geq0.
b
c
1
−
c
2
≥
0.
Prove that
10
(
a
2
+
b
2
+
c
2
−
b
c
3
)
≥
2
a
b
+
5
a
c
.
10(a^2+b^2+c^2-bc^3)\geq2ab+5ac.
10
(
a
2
+
b
2
+
c
2
−
b
c
3
)
≥
2
ab
+
5
a
c
.
inequalities
quadratics
analytic geometry
inequalities proposed