Question

Find the constant term (term independent of x) in the expansion of:
$\rm \bigg(\sqrt{x} - \frac{3}{x^{2}} \bigg)^{10}$

Answer 1

Solution :

Given ,

$\rm \bigg(\sqrt{x} - \frac{3}{x^{2}} \bigg)^{10}$

Tr+1 = 10Cr (√x )^10-r ( -3/x² )^r

= 10Cr × ( -3 )^r × [ x ^(10-r)/2- 2r ]

To find the term independent of x ,

put

(10-r)/2 - 2r = 0

=> (10-r -4r )/2 = 0

=> 10 - 5r = 0

=> -5r = -10

=> r = ( -10 )/( -5 )

=> r = 2

Therefore ,

T2+1 = T3

= 10C2 ( -3 )²

= 45 × 9

= 405

•••••

=> -2r = (