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2006 Romania National Olympiad
1
(x^3+1)(y^3+1) results in ugly ineq
(x^3+1)(y^3+1) results in ugly ineq
Source: RMO 2006
April 17, 2006
calculus
derivative
function
inequalities proposed
inequalities
Problem Statement
Find the maximal value of
(
x
3
+
1
)
(
y
3
+
1
)
,
\left( x^3+1 \right) \left( y^3 + 1\right) ,
(
x
3
+
1
)
(
y
3
+
1
)
,
where
x
,
y
ā
R
x,y \in \mathbb R
x
,
y
ā
R
,
x
+
y
=
1
x+y=1
x
+
y
=
1
. Dan Schwarz
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