若x^2y+xy^2+y^2z+yz^2+z^2x+zx^2+3xyz=k(x+y+z)*(xy+yz+zx),则k的值是
问题描述：
若x^2y+xy^2+y^2z+yz^2+z^2x+zx^2+3xyz=k(x+y+z)*(xy+yz+zx),则k的值是
答
左边=x^2y+xy^2+y^2z+yz^2+z^2x+zx^2+3xyz=(x^2y+xyz+zx^2)+(y^2x+xyz+zy^2)+(z^2y+xyz+xz^2)=x*(xy+yz+zx)+y*(xy+zx+yz)+z*(yz+xy+zx)=(x+y+z)*(xy+yz+zx)所以k=1另外简单的,将右边的(x+y+z)*(xy+yz+zx)直接展开得x...