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6
Triangle Ineq
Triangle Ineq
Source: Nice
January 6, 2005
inequalities
inequalities proposed
algebra
Problem Statement
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
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