已知x+y+z=3 xy+yz+zx=3 xyz=1求(x+y) (y+z)(z+x)

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已知x+y+z=3 xy+yz+zx=3 xyz=1求(x+y) (y+z)(z+x)

已知x+y+z=3 xy+yz+zx=3 xyz=1求(x+y) (y+z)(z+x)
已知x+y+z=3 xy+yz+zx=3 xyz=1求(x+y) (y+z)(z+x)

已知x+y+z=3 xy+yz+zx=3 xyz=1求(x+y) (y+z)(z+x)
(x+y) (y+z)(z+x)
=(3-z) (3-x)(3-y)
=(9-3x-3z+xz)(3-y)
=27-9y-9x+3xy-9z+3yz+3xz-xyz
=27-9(x+y+z)+3(xy+yz+xz)-xyz
=27-9*3+3*3-1
=27-27+9-1
=8