यदि `x=3+2sqrt(2)` है तो `(x^(6)+x^(4)+x^(2)+1)/(x^(3))` किसके बराबर है?

Options

A. 216
B. 192
C. 198
D. 204

Answer

D

Explanation

`x=3+2sqrt(2)`
`:. x=3-2sqrt(2)`
`x+1/x=3+2sqrt(2)+3-2sqrt(2)`
`x+1/x=6`
`(x+1/x)^(3)=(6)^(3)`
`x^(3)+1/(x^(3))+3xx6=216`
`x^(3)+1/(x^(3))+216-18=198`
`:. (x^(6)+x^(4)+x^(2)+1)/(x^(3))`
`=x^(3)+x+1/x+1/(x^(3))`
`= x^(3)+1/(x^(3))+x+1/x`
`=198+6=204`