已知x+y+z=3,x²+y²+z²=29,x³+y³+z³
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已知x+y+z=3,x²+y²+z²=29,x³+y³+z³=45,求xyz的值
![已知x+y+z=3,x²+y²+z²=29,x³+y³+z³](/uploads/image/z/20173167-63-7.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%2Bz%3D3%2Cx%26sup2%3B%2By%26sup2%3B%2Bz%26sup2%3B%3D29%2Cx%26sup3%3B%2By%26sup3%3B%2Bz%26sup3%3B)
(x^2+y^2+z^2-xy-yz-xz)(x+y+z)=x^3+y^3+z^3-3xyz
xy+yz+xz=[(x+y+z)^2-(x^2+y^2+z^2)]/2=-10
所以39*3=45-3xyz
xyz=-24
xy+yz+xz=[(x+y+z)^2-(x^2+y^2+z^2)]/2=-10
所以39*3=45-3xyz
xyz=-24
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