1/x+1/y+1/z=1/x^3+1/y^3+1/z^3+3/x^2y+3/xy^2+3/x^2z+3/xz^2+3/y^z+3/yz^2+6/xyz求1/x+1/y+1/z的值
网友回答
1/x+1/y+1/z=1/x³+1/y³+1/z³+3/(x²y)+3/(xy²)+3/(x²z)+3/(xz²)+3/(y²z)+3/(yz²)+6/(xyz)
1/x+1/y+1/z=(1/x+1/y+1/z)³
(1/x+1/y+1/z)³-(1/x+1/y+1/z)=0
(1/x+1/y+1/z)[(1/x+1/y+1/z)²-1]=0
(1/x+1/y+1/z)(1/x+1/y+1/z +1)(1/x+1/y+1/z -1)=0
1/x+1/y+1/z=0或1/x+1/y+1/z=-1或1/x+1/y+1/z=1
题目不难啊,关键是要知道：
1/x³+1/y³+1/z³+3/(x²y)+3/(xy²)+3/(x²z)+3/(xz²)+3/(y²z)+3/(yz²)+6/(xyz)=(1/x+1/y+1/z)³