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Mathematics
Mathematics
Problem
For real
k
k
k
, let
x
+
k
(
x
−
1
)
(
x
+
2
)
(
x
+
4
)
=
A
x
−
1
+
B
x
+
2
+
C
x
+
4
,
\frac{x+k}{(x-1)(x+2)(x+4)}=\frac{A}{x-1}+\frac{B}{x+2}+\frac{C}{x+4},
(
x
−
1
)
(
x
+
2
)
(
x
+
4
)
x
+
k
=
x
−
1
A
+
x
+
2
B
+
x
+
4
C
,
where
A
A
A
,
B
B
B
and
C
C
C
are constants. a. (i) If
A
=
2
A=2
A
=
2
, find the value of
k
k
k
. b. (ii) Using this value of
k
k
k
, determine
B
B
B
and
C
C
C
.
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