若x+y+z=6,xy+yz+zx=11,x^3+y^3+z^3-3xyz
问题描述：
若x+y+z=6,xy+yz+zx=11,x^3+y^3+z^3-3xyz
答
(x+y+z)²=6²
x²+y²+z²+2(xy+yz+zx)=36
x²+y²+z²=36-22=14
x³+y³+z³-3xyz
=(x³+3x²y+3xy²+y³+z³)-(3xyz+3x²y+3xy²)
=[(x+y)³+z³]-3xy(x+y+z)
=(x+y+z)(x²+y²+2xy-xz-yz+z²)-3xy(x+y+z)
=(x+y+z)(x²+y²+z²+2xy-3xy-xz-yz)
=(x+y+z)(x²+y²+z²-xy-yz-xz)
=18已知1/a+1/b=1/c求证,a^2+b^2+c^2=(a+b-c)^2什么叫过分知道吗？