Question

x的平方+x+1=0 求x的100次方+x的2001次方+x的3002次方=?

Answer 1

因为x^2+x+1=0,所以x^2=-x-1.

x^3=x*x^2=-x^2-x=-(-x-1)-x=1

x^100+x^2001+x^3002

=(x^3)^33*x+(x^3)^667+(x^3)^1000*x^2

=x+1+x^2

=0