Question

If the co-efficient of x^2 and x^ 3 are same in the expansion (3 + px) ^9, then the value of p is:-​

Answer 1

Answer:

Step-by-step explanation:

In the expansion of (a+b)  

n

 the (r+1)  

th

 term is  

T  

r+1

​  

=n  

C

​  

 

r

​  

a  

n−r

b  

r

 

General term in (3+ax)  

9

 is

T  

r+1

​  

=9  

C

​  

 

r

​  

3  

9−r

(ax)  

r

=9  

C

​  

 

r

​  

3  

9−r

a  

r

x  

r

 

Given that coefficient of x  

2

=co-efficient of x  

3

 

⇒9  

C

​  

 

2

​  

3  

9−2

a  

2

=9  

C

​  

 

3

​  

3  

9−3

a  

3

 

⇒a=  

9  

C

​  

 

3

​  

3  

9−3

 

9  

C

​  

 

2

​  

3  

9−2

 

​  

 

⇒a=  

9  

C

​  

 

3

​  

3  

6

 

9  

C

​  

 

2

​  

3  

7

 

​  

 

⇒a=  

3×2×1

9×8×7

​  

 

2×1

9×8

​  

 

​  

3  

7−6

=  

7

3×3

​  

=  

7

9

​