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.
问题描述：
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.
答
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
答
令P=x/(z+y)+y/(x+z)+z/(x+y)Px=x²/(z+y)+yx/(x+z)+zx/(x+y)①Py=xy/(z+y)+y²/(x+z)+zy/(x+y)②Pz=xz/(z+y)+yz/(x+z)+z²/(x+y)③①+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+...