यदि `(x+1/x)^(2)=3` है तो `(x^(72)+x^(66)+x^(54)+x^(24)+x^(6)+1)` का मान क्या होगा?

Options

A. 0
B. 1
C. 84
D. 206

Answer

A

Explanation

`(x+1/x)^(2)=3`
`x+1/x=sqrt(3)`
`impliesx^(3)+1/(x^(3))+3sqrt(3)+3sqrt(3)`
`implies x^(3)+1/(x^(3))=0`
`impliesx^(6)+1=0`
`impliesx^(6)=-1`
`impliesx^(72)+x^(66)+x^(54)+x^(24)+x^(6)+1`
`implies (x^(6))^(12)+(x^(6))^(11)+(x^(6))^(9)+(x^(6))^(4)+x^(6)+1`
`implies (-1)^(12)+(-1)^(11)+(-1)^(9)+(-1)^(4)+`
`-1+1`
`implies1-1-1+1-1+1=0`
`a+1/a=sqrt(3)`
`a^(6)=-1`
`:. a^(6)-1/(a^(6))+2=-1-1/((-1))+2`
`=-1+1+2=2`