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Romania National Olympiad
1999 Romania National Olympiad
2b
a^3+b^3+c^3 >= a+b+c if ab +be + ba <= 3abc 1999 Romania NMO VIII p2b
a^3+b^3+c^3 >= a+b+c if ab +be + ba <= 3abc 1999 Romania NMO VIII p2b
Source:
August 14, 2024
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
b
+
b
e
+
b
a
≤
3
a
b
c
ab +be + ba \le 3abc
ab
+
b
e
+
ba
≤
3
ab
c
. Prove that
a
3
+
b
3
+
c
3
≥
a
+
b
+
c
.
a^3+b^3+c^3 \ge a+b+c.
a
3
+
b
3
+
c
3
≥
a
+
b
+
c
.
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