Question

若x^3+x^2+x+1=0,则y=x^97+x^98+...+x^103的值是多少?

Answer 1

x^3+x^2+x+1=0,则（x+1）（x^2+1）=0,∴x=-1.

y=x^97+x^98+...+x^103=4×(-1)+3×1=-1.