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National and Regional Contests
Argentina Contests
Argentina Team Selection Test
2008 Argentina Team Selection Test
6
6
Part of
2008 Argentina Team Selection Test
Problems
(1)
Triangle Ineq
Source: Nice
1/6/2005
Show that in acute triangle ABC we have:
a
5
+
b
5
+
c
5
a
4
+
b
4
+
c
4
≥
3
R
\frac{a^5+b^5+c^5}{a^4+b^4+c^4} \ge \sqrt{3}R
a
4
+
b
4
+
c
4
a
5
+
b
5
+
c
5
≥
3
R
inequalities
inequalities proposed
algebra