Question

Evaluate the coefficient of x¹⁰ in the expansion of (3x+1/x²)¹²​

Answer 1

Answ144

→(1−2x+3x  

2

)(1+x)  

11

 

=(3x  

2

−2x+1)(1+x)  

11

 

General term of (1+x)  

11

 

T  

r+1

​

=  

11

C  

r

​

.x  

r

 

with 3x  

2

,r=9⇒coeff.=(  

11

C  

9

​

×3)

with −2x,r=10⇒coeff.=−2×  

11

C  

10

​

 

with 1,r=11⇒coeff=  

11

C  

11

​

 

⇒coeff.=  

11

C  

9

​

×3−2×11+1

=11.5.3−22+1

=11(5−2)+1=(11×13)+1

=143+1=144→(B) er:

Step-by-step explanation: