x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)(7-xy)＝10`……①
令x+y=t,
则(x+y)^2=t^2,
即x^2+y^2+2xy=t^2,
xy=(t^2-7)/2`,
代入①得`t(7-(t^2-7)/2)＝10`,
整理得：`t^3-21t+20=0`,
可因式分解得(`t-1)(t^2+t-20)=0`,
进一步分解得：`(t-1)(t+5)(t-4)=0`,
故解得t=1,4,-5
X+Yt=1,4,-5
x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)(7-xy)＝10`……①
令x+y=t,
则(x+y)^2=t^2,
即x^2+y^2+2xy=t^2,
xy=(t^2-7)/2`,
代入①得`t(7-(t^2-7)/2)＝10`,
整理得：`t^3-21t+20=0`,
可因式分解得(`t-1)(t^2+t-20)=0`,
进一步分解得：`(t-1)(t+5)(t-4)=0`,
故解得t=1,4,-5
X+Yt=1,4,-5