一道数学题已知xyz=1,求x/
x=1/yz;y=1/xz;z=1/xy;
x/xy+x+1 + y/yz+y+1 +z/zx+z+1
= (x/x)/((xy+x+xyz)/x) + (y/y)/((yz+y+xyz)/y) +(z/z)/((zx+z+xyz)/z)
= 1/y+1+yz + 1/z+1+xz + 1/x+1+xy
= 1/y+1+yz + (1*y)/((z+1+xz)*y) + (1*yz)/((x+1+xy)*yz)
= 1/y+1+yz + y/zy+y+xyz + yz/xyz+yz+xyzy
= 1/y+1+yz + y/zy+y+1 + yz/1+yz+y
= y+1+yz/y+1+yz...全部
x=1/yz;y=1/xz;z=1/xy;
x/xy+x+1 + y/yz+y+1 +z/zx+z+1
= (x/x)/((xy+x+xyz)/x) + (y/y)/((yz+y+xyz)/y) +(z/z)/((zx+z+xyz)/z)
= 1/y+1+yz + 1/z+1+xz + 1/x+1+xy
= 1/y+1+yz + (1*y)/((z+1+xz)*y) + (1*yz)/((x+1+xy)*yz)
= 1/y+1+yz + y/zy+y+xyz + yz/xyz+yz+xyzy
= 1/y+1+yz + y/zy+y+1 + yz/1+yz+y
= y+1+yz/y+1+yz
= 1。
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