已知x³-3x+2=0,求x²+1/x²的值
问题描述：
已知x³-3x+2=0,求x²+1/x²的值
答
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打错了是x²-3x+2=0x²-3x+2=0(x-1)(x-2)=0x=1或 2x=1时x²+1/x²=2x=2时x²+1/x²=17/4