यदि `x=sqrt(3)+sqrt(2)` है तो `x^(3)-1/(x^(3))` का मान ज्ञात करें।

Options

A. `10sqrt(2)`
B. `14sqrt(2)`
C. `22sqrt(2)`
D. `8sqrt(2)`

Answer

C

Explanation

`x=sqrt(3)+sqrt(2)`
`1/x=1/(sqrt(3)+sqrt(2))xx(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2))`
`1/x =sqrt(3)-sqrt(2)`
`x^(3)-1/(x^(3))=(x-1/x)^(3)+3xx x xx 1/x (x-1/x)`
`= (sqrt(3)+sqrt(2)-sqrt(3)+sqrt(2))^(3)+3sqrt(3)+sqrt(2)-sqrt(3)+sqrt(2))`
`=16sqrt(2)+6sqrt(2)= 22 sqrt(2)`