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x + y>=2 if x, y>0 with x + y + xy= 3 Austria Beginners' 2011 p3
x + y>=2 if x, y>0 with x + y + xy= 3 Austria Beginners' 2011 p3
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October 3, 2021
algebra
inequalities
Problem Statement
Let
x
,
y
x, y
x
,
y
be positive real numbers with
x
+
y
+
x
y
=
3
x + y + xy= 3
x
+
y
+
x
y
=
3
. Prove that
x
+
y
≥
2.
x + y\ge 2.
x
+
y
≥
2.
When does equality holds?(K. Czakler, GRG 21, Vienna)
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