Question

If the coefficient of x in (x^2+k/x)^5 is 270 then k is

Answer 1

Answer:

3

Step-by-step explanation:

Given  

If the coefficient of x in (x^2+k/x)^5 is 270 then k is  

ANSWER

.Now let r + 1 th term be in the expansion  

So T r + 1 = 270 x  

5 Cr (x^2)^5 – r (k/x)^r = 270 x

5 Cr (x^2)^5. (x^2)^-r . k^r.x^-r = 270 x

5 Cr . k^r. x^10 – 3r = 270.x^1

 Equating both sides we get

 x^1 = x^10 – 3 r and 270 = 5 Cr.k^r

 Since bases are same, exponents are equal.

  10 – 3 r = 1

   r = 9, r = 3

Substituting the value we get

  5 C 3 k^3 = 270

 So 5! / (5 – 3)! 3! k^3 = 270

  5 x 4 x 3 x 2 x 1 / 2 x 3 x 2 x 1 k^3 = 270

  10 k^3 = 270

   K^3 = 27

  k = 3