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A nice Inequality
A nice Inequality
Source:
October 22, 2010
inequalities
rearrangement inequality
inequalities unsolved
Problem Statement
For any positive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
, prove that
∑
c
y
c
l
i
c
(
b
+
c
)
(
a
4
−
b
2
c
2
)
a
b
+
2
b
c
+
c
a
≥
0
\sum_{cyclic} \frac{(b + c)(a^4 - b^2 c^2 )}{ab + 2bc + ca} \ge 0
cyc
l
i
c
∑
ab
+
2
b
c
+
c
a
(
b
+
c
)
(
a
4
−
b
2
c
2
)
≥
0
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