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Albania Contests
Albania JBMO TST
2015 Albania JBMO TST
5
5
Part of
2015 Albania JBMO TST
Problems
(1)
(3x-1)^2/x+(3y-1)^2/y >=1, for x,y>0, x+y=1 Austria Beginners' 2010 p3
Source:
10/3/2021
Let
x
x
x
and
y
y
y
be positive real numbers with
x
+
y
=
1
x + y =1
x
+
y
=
1
. Prove that
(
3
x
−
1
)
2
x
+
(
3
y
−
1
)
2
y
≥
1.
\frac{(3x-1)^2}{x}+ \frac{(3y-1)^2}{y} \ge1.
x
(
3
x
−
1
)
2
+
y
(
3
y
−
1
)
2
≥
1.
For which
x
x
x
and
y
y
y
equality holds?(K. Czakler, GRG 21, Vienna)
function