⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?

题目

⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?
分类讨论的题、2种

答案

因为x/(y+z)=y/(x+z)=z/(x+y）=k所以x=k(y+z)y=k(x+z)z=k(x+y)以上三式相加得：x+y+z=k(y+z)+k(x+z)+k(x+y)x+y+z=k(2x+2y+2z)x+y+z=2k(x+y+z)分类讨论：当x+y+z不等于0时以上左右等式可以同时消去x+y+z则2k=1k=1/2当...