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2020 Azerbaijan National Olympiad
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Problem 3
Problem 3
Source: Azerbaijan third round 2020
June 6, 2020
inequalities
algebra
Problem Statement
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive numbers.
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
Prove that:
∑
a
2
+
6
2
a
2
+
2
b
2
+
2
c
2
+
2
a
−
1
≤
3
\sum \frac{a^2+6}{2a^2+2b^2+2c^2+2a-1}\leq 3
∑
2
a
2
+
2
b
2
+
2
c
2
+
2
a
−
1
a
2
+
6
≤
3
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