Question

x+1/x=-1怎么推出x的三次方等于1?同理x+1/x=1怎么推出x的三次方等于-1?

Answer 1

x+1/x=-1

x^2+1=-x

x^2+x+1=0

(x-1)(x^2+x+1)=0

x^3-1=0

x^3=1

x+1/x=1

x^2+1=x

x^2-x+1=0

(x+1)(x^2-x+1)=0

x^3+1=0

x^3=-1