已知x+y+z=3,x^2+y^2+z^2=19,x^3+y^3+z^3=30 则xyz=
问题描述：
已知x+y+z=3,x^2+y^2+z^2=19,x^3+y^3+z^3=30 则xyz=
答
牢记一个基本的公式:x^3+y^3+z^3-3xyz =(x+y+z)(x^2+y^2+z^2-xy-yz-zx) =(x+y+z)[(x+y+z)^2-3(xy+yz+zx)] 所以:根据x+y+z=3,两边平方,有:x^2+y^2+z^2+2xy+2yz+2zx=9.再有:x^2+y^2+z^2=19,所以:xy+yz+yz=-5.所以代入...