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Rioplatense Mathematical Olympiad, Level 3
2002 Rioplatense Mathematical Olympiad, Level 3
4
4
Part of
2002 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
(a+b)/c^2+(c+a)/b^2+(b+c)/a^2 >= 9/(a+b+c) +1/a + 1/b + 1/c
Source: Rioplatense Olympiad 2002 level 3 P4
9/6/2018
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive real numbers. Show that
a
+
b
c
2
+
c
+
a
b
2
+
b
+
c
a
2
≥
9
a
+
b
+
c
+
1
a
+
1
b
+
1
c
\frac{a+b}{c^2}+ \frac{c+a}{b^2}+ \frac{b+c}{a^2}\ge \frac{9}{a+b+c}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}
c
2
a
+
b
+
b
2
c
+
a
+
a
2
b
+
c
≥
a
+
b
+
c
9
+
a
1
+
b
1
+
c
1
algebra
Inequality
3-variable inequality
inequalities