Question

已知x2+x+1=0,求x4+1/x4的值

Answer 1

x^2+x+1=0,x不等于0

方程两边÷x,

x+1+1/x=0

x+1/x=-1

(x+1/x)^2=1

x^2+1/x^2+2=1

x^2+1/x^2=-1

X^4+1/X^4

=（X^2+1/X^2）^2-2

=（-1)^2-2

=-1