Question

Coefficient of x^4 in expansion (x/2-3/x^2)^10.

Answer 1

Given: The term (x/2-3/x^2)^10

To find: Coefficient of x^4 in expansion (x/2-3/x^2)^10

Solution:

• Now the general term of expansion (a+b)^n is given by:

            then T(r+1) = n C r (a)^ n-r x (b)^ r

• So we have the term (x/2-3/x^2)^10, expansion will be:

            T(r+1) = 10 C r (x/2)^ n-r x (-3/x^2)^ r

                      = (-1)^r x (10 C r) x (2)^r-10 x (3)^r x (x)^ 10-r-2r

• So now we want the coefficient of x^4, so

            10-3r = 4

            6 = 3r

            r = 2

• So now put the value of r in the expansion, we get:

            (-1)^2 x (10 C 2) x (2)^2-10 x (3)^2 x (x)^ 10-2-4

         = 10 C 2 x 2^-8 x 3^2

         = 10 C 2 x 2^-8 x 9

         = 45 x 9 / 256

         = 405/256

Answer:

           So the coefficient of x^4 in expansion (x/2-3/x^2)^10 is 405/256.

Answer 2

Step-by-step explanation:

here i hv attached the ans