已知x³-3x+2=0,求x²+1/x²的值

已知x³-3x+2=0,求x²+1/x²的值
已知x³-3x+2=0,求x²+1/x²的值

已知x³-3x+2=0,求x²+1/x²的值
x³-3x+2=0
x³-x²+x²-3x+2=0
x²(x-1)+(x-1)(x-2)=0
(x-1)(x²+x-2)=0
(x-1)²(x+2)=0
∴x=1,-2
当x=1时,x²+1/x²=2
当x=-2时,x²+1/x²=17/4

2 17/4