∵x3-y3=（x-y）（x2+xy+y2）=2，x-y=1，x3-y3=（x-y）（x2+xy+y2）=2，又∵x2-2xy+y2=1，与上式联立得：xy=13，x2+y2=53，故x4+y4=（x2+y2）2-2x2y2=239，又x5-y5=x5-x4y+x4y-xy4+xy4-y5=x4（x-y）+xy（x3-y3）+y4...