已知x+y+z=5,且x^2+y^2+z^2=3,求xy+yz+xz的值

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已知x+y+z=5,且x^2+y^2+z^2=3,求xy+yz+xz的值
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已知x+y+z=5,且x^2+y^2+z^2=3,求xy+yz+xz的值
已知x+y+z=5,且x^2+y^2+z^2=3,求xy+yz+xz的值

已知x+y+z=5,且x^2+y^2+z^2=3,求xy+yz+xz的值
x+y+z=5
两边平方得
x^2+y^2+z^2+2(xy+yz+xz)=25
3+2(xy+yz+xz)=25
2(xy+yz+xz)=22
xy+yz+xz=11

(x+y+z)^2-(x^2+y^2+z^2)=25-3=22
=2(xy+yz+xz)
xy+yz+xz=22/2=11