Question

已知:x2+x-1=0,不解方程求x3-1/x3

Answer 1

因为x²＋x－1＝0,知x≠0,所以两边同除以x得,x-1/x=-1

x³－1/x³=(x-1/x)(x²＋1/x²-2+3)=(x-1/x)³+3(x-1/x)=-1³+3*(-1)=-4