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2009 JBMO Shortlist
2
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Mathenatics
Source: JBMO 2009 Shortlist
May 3, 2016
algebra
Problem Statement
A
2
\boxed{A2}
A
2
Find the maximum value of
z
+
x
z+x
z
+
x
if
x
,
y
,
z
x,y,z
x
,
y
,
z
are satisfying the given conditions.
x
2
+
y
2
=
4
x^2+y^2=4
x
2
+
y
2
=
4
z
2
+
t
2
=
9
z^2+t^2=9
z
2
+
t
2
=
9
x
t
+
y
z
≥
6
xt+yz\geq 6
x
t
+
yz
≥
6
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