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Albania IMO TST inequality
Albania IMO TST inequality
Source:
May 18, 2013
inequalities
inequalities proposed
Problem Statement
Find the greatest value of the expression
1
x
2
−
4
x
+
9
+
1
y
2
−
4
y
+
9
+
1
z
2
−
4
z
+
9
\frac{1}{x^2-4x+9}+\frac{1}{y^2-4y+9}+\frac{1}{z^2-4z+9}
x
2
−
4
x
+
9
1
+
y
2
−
4
y
+
9
1
+
z
2
−
4
z
+
9
1
where
x
x
x
,
y
y
y
,
z
z
z
are nonnegative real numbers such that
x
+
y
+
z
=
1
x+y+z=1
x
+
y
+
z
=
1
.
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