Izwestno sto x^2+x+1=0 nayti x^14+x^-14, x^15+x^-15

Question

Izwestno sto x^2+x+1=0
nayti x^14+x^-14, x^15+x^-15

Answer 1

X^2+x+1=0, тогда х^2+х=-1.
x(x+1)=-1
(x+1)(x^2-x+1)=x^3+1.
X^3=-1
X=-1

X^14+x^-14=-1^14+1/-1^14=2
X^15+x^-15=-1-1=-2