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2010 Regional Competition For Advanced Students
1
Inequality with 0≤a,b≤1
Inequality with 0≤a,b≤1
Source:
April 26, 2010
inequalities
trigonometry
inequalities proposed
Problem Statement
Let
0
≤
a
0 \le a
0
≤
a
,
b
≤
1
b \le 1
b
≤
1
be real numbers. Prove the following inequality:
a
3
b
3
+
(
1
−
a
2
)
(
1
−
a
b
)
(
1
−
b
2
)
≤
1.
\sqrt{a^3b^3}+ \sqrt{(1-a^2)(1-ab)(1-b^2)} \le 1.
a
3
b
3
+
(
1
−
a
2
)
(
1
−
ab
)
(
1
−
b
2
)
≤
1.
(41th Austrian Mathematical Olympiad, regional competition, problem 1)
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