Question

一道代数题目，帮我解答一下，谢谢

已知：x^2/(z+y)+y^2/(x+z)+z^2/(x+y)=0，求x/(z+y)+y/(x+z)+z/(x+y)的值.

Answer 1

令P=x/(z+y)+y/(x+z)+z/(x+y)
Px=x²/(z+y)+yx/(x+z)+zx/(x+y)①
Py=xy/(z+y)+y²/(x+z)+zy/(x+y)②
Pz=xz/(z+y)+yz/(x+z)+z²/(x+y)③
①+②+③得
xp+yp+zp=(x^2/z+y)+(y^2/x+z)+(z^2/x+y)+x+y+z=0+x+y+z=x+y+z
即（x+y+z)p=x+y+z
x+y+z≠0
故p=1

Answer 2

令P=待求值
计算得xp+yp+zp=(x^2/z+y)+(y^2/x+z)+(z^2/x+y)+x+y+z=0+x+y+z=x+y+z
即（x+y+z)p=x+y+z
我想x+y+z非0
故p=1