已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.各路神通,

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已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.各路神通,已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.各路神通,已知x-y=1,x3-y3=2,求x4+y4及x5-y5

已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.各路神通,
已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.
各路神通,

已知x-y=1,x3-y3=2,求x4+y4及x5-y5的值.各路神通,
∵x3-y3=(x-y)(x2+xy+y2)=2,
x2+xy+y2=2
x-y=1,
又∵x2-2xy+y2=1,
与上式联立得:
xy= 1/3,x2+y2= 5/3,
故x4+y4=(x2+y2)2-2x2y2= 23/9,
又x5-y5=x5-x4y+x4y-xy4+xy4-y5=x4(x-y)+xy(x3-y3)+y4(x-y),
将x-y=1,xy= 1/3,x3-y3=2代入,
可得x5-y5= 29/9,