X
In the expansion of (k+x)^8, the coefficient of x^5 is 10 times the coefficient of x^6. Find
the value of k.
Answers
Answered by
2
Step-by-step explanation:
Calculate the binomial coefficient and appropriate powers of
2
and
3
to find that the required coefficient is:
1088640
Explanation:
(
2
x
+
3
)
10
=
10
∑
k
=
0
(
10
k
)
2
10
−
k
3
k
x
10
−
k
The term in
x
6
is the one for
k
=
4
, so has coefficient:
(
10
4
)
2
6
⋅
3
4
=
10
!
4
!
6
!
⋅
64
⋅
81
=
10
×
9
×
8
×
7
4
×
3
×
2
×
1
⋅
64
⋅
81
=
210
⋅
64
⋅
81
=
1088640
Instead of calculating
(
10
4
)
, you can pick it out from the appropriate row of Pascal's triangle...
enter image source here
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