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2007 Harvard-MIT Mathematics Tournament
19
19
Part of
2007 Harvard-MIT Mathematics Tournament
Problems
(1)
2007 Guts #19: Wacky Multivariable Function
Source:
6/22/2012
Define
x
⋆
y
=
x
2
+
3
x
y
+
y
2
−
2
x
−
2
y
+
4
x
y
+
4
x\star y=\frac{\sqrt{x^2+3xy+y^2-2x-2y+4}}{xy+4}
x
⋆
y
=
x
y
+
4
x
2
+
3
x
y
+
y
2
−
2
x
−
2
y
+
4
. Compute
(
(
⋯
(
(
2007
⋆
2006
)
⋆
2005
)
⋆
⋯
)
⋆
1
)
.
((\cdots ((2007\star 2006)\star 2005)\star\cdots )\star 1).
((
⋯
((
2007
⋆
2006
)
⋆
2005
)
⋆
⋯
)
⋆
1
)
.
function