Physics, asked by skaur320, 2 months ago

(3+5x)^4 solve by binomial theorem​

Answers

Answered by HandsomeHunkk
0

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.

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