If and are the roots of x²-x+1=0, then the equation whose roots are ¹⁰⁰ and ¹⁰⁰ are

Step-by-step solution

We have x³+1 (x+1) (x²-x+1 ) . Therefore, and are the complex cube roots of -1 so that we may take =- and =- ², where 1 is a cube root of unity. Thus ¹⁰⁰=(- )¹⁰⁰= and ¹⁰⁰= (- ² )¹⁰⁰= ², so that the required equation is x ²+ x +1=0