Question

已知x+y+z=3,x^2+y^2+z^2=19,x^3+y^3+z^3=30 则xyz=

Answer 1

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.

所以代入上面的公式,有:

30-3xyz=3*[3*3-3*(-5)]

所以xyz=-14