已知x+y+z=1,xy+yz+zx=2,xyz2,求x2(y+z)+y2(z+x)+z2(x+y)的值已知x+y+z=1,xy+yz+zx=2,xyz2,求x²(y+z)+y²(z+x)+z²(x+y)的值

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已知x+y+z=1,xy+yz+zx=2,xyz2,求x2(y+z)+y2(z+x)+z2(x+y)的值已知x+y+z=1,xy+yz+zx=2,xyz2,求x²(y+z)+y²(z+x)+z²(x+y)的值

已知x+y+z=1,xy+yz+zx=2,xyz2,求x2(y+z)+y2(z+x)+z2(x+y)的值已知x+y+z=1,xy+yz+zx=2,xyz2,求x²(y+z)+y²(z+x)+z²(x+y)的值
已知x+y+z=1,xy+yz+zx=2,xyz2,求x2(y+z)+y2(z+x)+z2(x+y)的值
已知x+y+z=1,xy+yz+zx=2,xyz2,求x²(y+z)+y²(z+x)+z²(x+y)的值

已知x+y+z=1,xy+yz+zx=2,xyz2,求x2(y+z)+y2(z+x)+z2(x+y)的值已知x+y+z=1,xy+yz+zx=2,xyz2,求x²(y+z)+y²(z+x)+z²(x+y)的值
x+y+z=1
xy+yz+zx=2
1*2
=(x+y+z)(xy+yz+zx)
=x(xy+yz+zx)+y(xy+yz+zx)+z(xy+yz+zx)
=x²y+xyz+zx²+xy²+y²z+xyz+xyz+yz²+z²x
=x²(y+z)+y²(z+x)+z²(x+y)+3xyz
=x²(y+z)+y²(z+x)+z²(x+y)+6
∴x²(y+z)+y²(z+x)+z²(x+y)
=2-6=-4