已知 x/(y+z)+y/(z+x)+z/(x+y)=1求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)_数学解答

已知 x/(y+z)+y/(z+x)+z/(x+y)=1
求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)=?

人气：289 ℃　时间：2020-02-03 05:36:05

解答

因为x/y+z + y/z+x +z/x+y=1 所以x/y+z=1-y/z+x-z/x+y,两边同乘以x 得x^2/y+z=x-xy/z+x-xz/x+y 同理y^2/x+z=y-xy/z+y-yz/x+y,z^2=z-xz/y+z-yz/x+z 所以原式=x+y+z-(xy+zy)/x+z-(xz+yz)/x+y-(yx+zx)/y+z =x+y+z-y-z-x...