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Putnam
1984 Putnam
B2
Minimum value
Minimum value
Source: Putnam 1984
May 20, 2006
calculus
conics
hyperbola
Problem Statement
Find the minimum value of
(
u
−
v
)
2
+
(
2
−
u
2
−
9
v
)
2
(u-v)^2+\left(\sqrt{2-u^2}-\frac{9}{v}\right)^2
(
u
−
v
)
2
+
(
2
−
u
2
−
v
9
)
2
for
0
<
u
<
2
0<u<\sqrt{2}
0
<
u
<
2
and
v
>
0
v>0
v
>
0
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