Question

The coefficient if x^2 in the expansion of ( 2x + k )^6 is equal to the coefficient of x^5 in the expansion of ( 2 + kx )^8 . Find k​

Answer 1

Answer:

The term containing x^2 in (2x + k)^6 is

= 6C4 (2x)^(6-4) k^4

= 6C4 (2x)^2 k^4

= 6C4 4k^4 x^2

= 15*4k^4 x^2

60 k^4 x^2

coefficient of x^2 = 60 k^4

now,

the term containing x^5 in (2 + Kx)^8 is

8C5 2^(8-5). (Kx)^5

56 2^3 k^5 x^5

56*8 k^5 x^5

448 k^5 x^5

coefficient of x^5

448 k^5

as per question

448 k^5 = 60 k^4

k = 60/448

k = 15/112