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Swedish Mathematical Competition
2013 Swedish Mathematical Competition
6
6
Part of
2013 Swedish Mathematical Competition
Problems
(1)
a^2>3b if a^2b^2 + 18 abc > 4b^3+4a^3c+27c^2
Source: 2013 Swedish Mathematical Competition p6
4/30/2021
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
, be real numbers such that
a
2
b
2
+
18
a
b
c
>
4
b
3
+
4
a
3
c
+
27
c
2
.
a^2b^2 + 18 abc > 4b^3+4a^3c+27c^2 .
a
2
b
2
+
18
ab
c
>
4
b
3
+
4
a
3
c
+
27
c
2
.
Prove that
a
2
>
3
b
a^2>3b
a
2
>
3
b
.
inequalities
algebra