यदि `x+1/x=sqrt(3)` है तो `x^(18)+x^(12)+x^(6)+1` का मान ज्ञात करें।

Options

A. 0
B. 1
C. 2
D. 3

Answer

A

Explanation

`x+1/x=sqrt(3)` take cube on both sides
`(x+1/x)^(3)=(sqrt(3))^(3)`
`x^(3)+1/(x^(3))+3x xx 1/x(x+1/x)=3sqrt(3)`
`implies x^(3)+1/(x^(3))+3(sqrt(3))=3sqrt(3)`
`x^(3)+1/(x^(3))=0`
`:. x^(6)=-1`
`:. x^(18)+x^(12)+x^(6)+1`
`=(-1)^(3)+(-1)^(2)+(-1)+1`
`=-1+1-1+1=0`