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已知x^2+y^2+z^2=8,xy+yz+xz=4.则(x+y+z)^2=
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已知x^2+y^2+z^2=8,xy+yz+xz=4.则(x+y+z)^2=
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答案和解析
(x+y+z)^2
=(x+y)²+z²+2(x+y)z
=x²+y²+2xy+z²+2xz+2yz
=x²+y²+z²+2(xy+yz+xz)
=8+2*4
=16
=(x+y)²+z²+2(x+y)z
=x²+y²+2xy+z²+2xz+2yz
=x²+y²+z²+2(xy+yz+xz)
=8+2*4
=16
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