What is the coefficient of x in the expression ax³ + bx² + d?
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General term T
r+1
in the expansion of (a+b)
n
is given by
T
r+1
=
n
C
r
a
n−r
b
r
Applying to (ax
2
+
bx
1
)
11
, we get
T
r+1
=
11
C
r
x
22−3r
a
11
(ab)
−r
...(i)
Therefore 22−3r=7 for coefficient of x
7
⇒r=5
Thus, (i) reduces to
T
6
=
11
C
5
x
7
a
11
(ab)
−5
Similarly applying to (ax−
bx
2
1
)
11
, we get
T
r+1
=(−1)
r
11
C
r
x
11−3r
a
11
(ab)
−r
...(ii)
Therefore 11−3r=−7 for coefficient of x
−7
⇒r=6
Equation (ii) reduces to
T
7
=
11
C
6
x
−7
a
11
ab
−6
...(b)
Hence applying the given condition we get
11
C
6
a
11
(ab)
−6
=
11
C
5
a
11
(ab)
−5
from(a,b)
ab=1
Please solve like this.
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