Question

Find the term independent of x in the expansion of (2x - 1/x)10​

Answer 1

Answer:

Step-by-step explanation:

  Tr + 1 = 12cr .(3x)12 – r .(-1 / 2x2)

            = 12cr .(3)12 – r ( x )12 – r . (- 1 /2) r. 1/x2 ) r

            = 12cr . (3)12 – r. (- 1 / 2) r ( x )12 – r. ( x ) – 2r

            = 12cr . (3)12 – r. (- 1 / 2) r . ( x ) 12 – 3r ….………….. (D)

Since we need a term independent of x, which means the power of x must be 0, we will set the power 12 – 3r of x in (D) above to 0.  

12 – 3r = 0, 3r = 12, r = 4

Answer 2

Term independent of x index of the means index of the term should be zero.
first we will find the general term.
Tr+1= 10Cr(2x)^10-r(-1/x)^r
solve this and you will get index of x=10-2r
put 10-2r=0
r=5
if r=5then term will be 6th
put r=5 in the general term
and you will get T6= -4032



hope it helps you