यदि `x^(2)+1/(x^(2))=1` है तो `x^(102)+x^(96)+x^(90)+x^(84)+x^(78)+x^(72)+5` का मान क्या होगा?

Options

A. 0
B. 5
C. 3
D. 1

Answer

B

Explanation

If `x^(2)+1/(x^(2))=1`
Then `x+1/x=sqrt(3)`
`implies x^(3)+1/(x^(3))=(sqrt(3))^(3)-3sqrt(3)=0`
`implies x^(6)=-1` or `x^(6)+1=0`
then
`x^(102)+x^(96)+x^(90)+x^(94)+x^(78)+x^(72)+5`
`x^(96)(x^(6)+1)+x^(84)(x^(6)+1)+x^(72)(x^(6)+1)+5=5`