x^3=y+7,y^3=x+7(x≠y),求x^3-2xy+y^3的值我不知道2009,你的解题步骤到(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14就完全看不懂了，（x+y)^2+1=xy?“(*)只有一个实根，用matlab解”我也完全听不懂

x^3=y+7,y^3=x+7(x≠y),求x^3-2xy+y^3的值我不知道2009,你的解题步骤到(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14就完全看不懂了，（x+y)^2+1=xy?“(*)只有一个实根，用matlab解”我也完全听不懂
x^3=y+7,y^3=x+7(x≠y),求x^3-2xy+y^3的值
我不知道2009,你的解题步骤到(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14就完全看不懂了，（x+y)^2+1=xy?“(*)只有一个实根，用matlab解”我也完全听不懂

x^3=y+7,y^3=x+7(x≠y),求x^3-2xy+y^3的值我不知道2009,你的解题步骤到(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14就完全看不懂了，（x+y)^2+1=xy?“(*)只有一个实根，用matlab解”我也完全听不懂
x^3-y^3=y-x
(x-y)(x^2+xy+y^2)=(y-x)
x^2+xy+y^2=-1
(x+y)^2-xy=-1 (1)
x^3+y^3=x+y+14
(x+y)(x^2-xy+y^2-1)=14
(x+y)((x+y)^2-3xy-1)=14
(x+y)^3-(3xy+1)(x+y)=14
(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14
(x+y)^3-(3(x+y)^2+4)(x+y)=14
-2(x+y)^3-4(x+y)=14
(x+y)^3+2(x+y)+7=0 （*）
x^3-2xy+y^3=(x+y)(x^2-xy+y^2)-2xy
=(x+y)^3-3xy(x+y)-2xy=(x+y)^3-(3(x+y)^2+3)(x+y)-2(x+y)^2-2=-2(x+y)^3-2(x+y)^2-3(x+y)-2=4(x+y)+14-2(x+y)^2-3(x+y)-2=(x+y)-2(x+y)^2+12
(*)只有一个实根,用matlab解
看(1)式
x+y=-1/6*(756+12*4065^(1/2))^(1/3)+4/(756+12*4065^(1/2))^(1/3)
代进去算原式的值~
得到还是用matlab算吧
算出来是这个-1/6*(756+12*4065^(1/2))^(1/3)+4/(756+12*4065^(1/2))^(1/3)-2*(-1/6*(756+12*4065^(1/2))^(1/3)+4/(756+12*4065^(1/2))^(1/3))^2+12
晕死了,大概我变形变错了吧.-_-!
我觉得最最傻的思路就是上面了,把所有式子对称化(就是都用x+y和xy把原先的式子表示出来,把x+y,xy解出来代进去,得到答案.

x^3-y^3=y-x
(x-y)(x^2+xy+y^2)=(y-x)
x^2+xy+y^2=-1
(x+y)^2-xy=-1
x^3+y^3=x+y+14
(x+y)(x^2-xy+y^2-1)=14
(x+y)((x+y)^2-3xy-1)=14
(x+y)^3-(3xy+1)(x+y)=14
(x+y)^3-(3...

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x^3-y^3=y-x
(x-y)(x^2+xy+y^2)=(y-x)
x^2+xy+y^2=-1
(x+y)^2-xy=-1
x^3+y^3=x+y+14
(x+y)(x^2-xy+y^2-1)=14
(x+y)((x+y)^2-3xy-1)=14
(x+y)^3-(3xy+1)(x+y)=14
(x+y)^3-(3(x+y)^2+1)+1)(x+y)=14
(x+y)^3-(3(x+y)^2+4)(x+y)=14
-2(x+y)^3-12(x+y)=14
(x+y)^3+6(x+y)+7=0
(x+y+1)((x+y)^2-(x+y)+7)=0
((x+y)^2-(x+y)+7)>0
x+y+1=0
x+y=-1
xy=2
x^3-2xy+y^3=(x+y)(x^2-xy+y^2)-2xy
=(x+y)^3-3xy(x+y)-2xy=-1+3*2-4=1

收起

x^3=y+7 .............(1)
y^3=x+7 .............(2)
(1)-(2)得,x^3-y^3=(x-y)(x^2+xy+y^2)=y-x,
故(x^2+xy+y^2)=-1,

1. x^2-x=7,y^2-y=7
所以x^2=x+7,y^2=y+7
x^2-x-(y^2-y)=(x^2-y^2)-(x-y)=(x+y)(x-y)-(x-y)
=(x-y)(x+y-1)=0
因为x不等于y,所以x+y=1
x^3+x^2y+xy^2+y^3+2xy=x(x+7)+(x+7)y+x(y+7)+(y+7)y
=(x+7)(x+y)+(y+7)(x+y)=(x+y)(x+y+14)=15

x^3-2xy+y^3
=(y+7)-2xy+(x+7)
=x+y-2xy+14

楼上的明显是错的啊！
把x+y=-1
xy=2
带入(x+y)((x+y)^2-3xy-1)=14
显然不成立啊！

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