已知XYZ互不等,X+Y+Z=1求证(1/X-1)(1/Y-1)(1/Z-1)>8
热心网友
还缺条件X,Y,Z是正数，否则如X=-6,Y=3,Z=4,不等式不成立证明:X0,Y0,Z0,X+Y+Z=1,X,Y,Z互不相等(1/X-1)(1/Y-1)(1/Z-1)=[(X+Y+Z)/X-1][(X+Y+Z)/Y-1][(X+Y+Z)/Z-1]=(Y+Z)(X+Z)(X+Y)/(XYZ)2√(YZ)*2√(XZ)*2√(XY)/(XYZ)=8
已知XYZ互不等,X+Y+Z=1求证(1/X-1)(1/Y-1)(1/Z-1)>8
还缺条件X,Y,Z是正数，否则如X=-6,Y=3,Z=4,不等式不成立证明:X0,Y0,Z0,X+Y+Z=1,X,Y,Z互不相等(1/X-1)(1/Y-1)(1/Z-1)=[(X+Y+Z)/X-1][(X+Y+Z)/Y-1][(X+Y+Z)/Z-1]=(Y+Z)(X+Z)(X+Y)/(XYZ)2√(YZ)*2√(XZ)*2√(XY)/(XYZ)=8