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National and Regional Contests
Poland Contests
Poland - Second Round
1996 Poland - Second Round
3
Poland97?
Poland97?
Source:
November 19, 2006
function
inequalities
Hi
Problem Statement
a
,
b
,
c
≥
−
3
/
4
a,b,c \geq-3/4
a
,
b
,
c
≥
−
3/4
and
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Show that:
a
1
+
a
2
+
b
1
+
b
2
+
c
1
+
c
2
≤
9
10
\frac{a}{1+a^{2}}+\frac{b}{1+b^{2}}+\frac{c}{1+c^{2}}\leq \frac{9}{10}
1
+
a
2
a
+
1
+
b
2
b
+
1
+
c
2
c
≤
10
9
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