(3+5x)^4 solve by binomial theorem
Answers
Now on to the binomial.
We will use the simple binomial a+b, but it could be any binomial.
(a+b)2 = (a+b)(a+b) = a2 + 2ab + b2
(a+b)3 = (a2 + 2ab + b2)(a+b) = a3 + 3a2b + 3ab2 + b3
a3 + 3a2b + 3ab2 + b3
Now, notice the exponents of a. ...
Likewise the exponents of b go upwards: 0, 1, 2, 3:
(3
−x/4
+3
5x/4
)
n
=∑
r=0
n
n
C
r
(3
−x/4
)
n−r
.(3
5x/4
)
n−r
We know that sum of binomial coefficient =2
n
⇒2
n
=6
4
⇒n=6
Third term, T
3
=
6
C
2
(3
−x/4
)
4
.(3
5x/4
)
2
⇒15×3
(−x+5x/2)
=15.(3
3x/2
)
Term with greatest binomial coefficient will be the middle term ; i.e. T
4
⇒T
4
=
6
C
3
(3
−x/4
)
3
.(3
5x/4
)
3
=20.3
3x
Given that, 20.3
3x
−15.3
3x/2
=6−1=5.
Solving the above equation by taking (3
3x/2
) as y.
We get x=0.
Hence, the answer is 0.