已知x2-3x=1 =0,求x3+1/x3
问题描述：
已知x2-3x=1 =0,求x3+1/x3
答
x2-3x+1 =0
除以x得 x-3+1/x=0
x+1/x=3
x³+1/x³=(x+1/x)(x²-1+1/x²)
=3×[(x²+2+1/x²)-1-2]
=3×[(x+1/x)²-3]
=3×﹙3²-3)
=18