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Kosovo National Mathematical Olympiad
2010 Kosovo National Mathematical Olympiad
5
5
Part of
2010 Kosovo National Mathematical Olympiad
Problems
(1)
Kosovo MO 2010 Problem 5
Source: Kosovo MO 2010 Problem 5
6/7/2021
Let
x
,
y
x,y
x
,
y
be positive real numbers such that
x
+
y
=
1
x+y=1
x
+
y
=
1
. Prove that
(
1
+
1
x
)
(
1
+
1
y
)
≥
9
\left(1+\frac {1}{x}\right)\left(1+\frac {1}{y}\right)\geq 9
(
1
+
x
1
)
(
1
+
y
1
)
≥
9
.
Inequality
algebra
inequalities proposed
inequalities