यदि `x+(1)/(x)=1` तो सिद्ध कीजिए कि `x^(2000)+(1)/(x^(2000))=-1`

Explanation

दिया है `x+(1)/(x)=1rArrx^(2)-x+1=0`
इसलिए `x=(1pmsqrt(3)i)/(2)=-omega,-omega^(2)`
`rArrx^(2000)+(1)/(x^(2000))={(omega^(2000)+(1)/(omega^(2000))=omega^(2)+(1)/(omega^(2))=omega^(2)+omega=-1",यदि "x=-omega),(omega^(4000)+(1)/(omega^(4000))=omega+(1)/(omega)=omega+omega^(2)=-1", यदि "x=-omega^(2)):} `