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2014 BMT Spring
14
BMT 2014 Spring - Individual 14
BMT 2014 Spring - Individual 14
Source:
January 22, 2022
algebra
Problem Statement
Suppose that
f
(
x
)
=
x
x
2
−
2
x
+
2
f(x) = \frac{x}{x^2 - 2x + 2}
f
(
x
)
=
x
2
−
2
x
+
2
x
and
g
(
x
1
,
x
2
,
.
.
.
,
x
7
)
=
f
(
x
1
)
+
f
(
x
2
)
+
.
.
.
+
f
(
x
7
)
g(x_1, x_2, ... , x_7) = f(x_1) + f(x_2) +... + f(x_7)
g
(
x
1
,
x
2
,
...
,
x
7
)
=
f
(
x
1
)
+
f
(
x
2
)
+
...
+
f
(
x
7
)
. If
x
1
,
x
2
,
.
.
.
,
x
7
x_1, x_2,..., x_7
x
1
,
x
2
,
...
,
x
7
are non-negative real numbers with sum
5
5
5
, determine for how many tuples
(
x
1
,
x
2
,
.
.
.
,
x
7
)
(x_1, x_2, ... , x_7)
(
x
1
,
x
2
,
...
,
x
7
)
does
g
(
x
1
,
x
2
,
.
.
.
,
x
7
)
g(x_1, x_2, ... , x_7)
g
(
x
1
,
x
2
,
...
,
x
7
)
obtain its maximal value.
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