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Mathematics
Mathematics
Problem
Define
P
(
x
)
=
(
x
+
1
x
)
10
P(x)=\left(x+\dfrac{1}{x}\right)^{10}
P
(
x
)
=
(
x
+
x
1
)
10
and
Q
(
x
)
=
(
x
−
1
x
)
10
Q(x)=\left(x-\dfrac{1}{x}\right)^{10}
Q
(
x
)
=
(
x
−
x
1
)
10
. a. (i) Show that each of
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
contains a term that is independent of
x
x
x
. b. (ii) Find individually the independent terms in
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
. c. (iii) Hence compute the value of
P
(
1
)
+
Q
(
1
)
P(1)+Q(1)
P
(
1
)
+
Q
(
1
)
.
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