x-y-z=3.yz-xy-xz=3.则x²+y²+z²=?
问题描述：
x-y-z=3.yz-xy-xz=3.则x²+y²+z²=?
答
(x-y-z)²=9
(x-y)²+z²-2z(x-y)=9
x²+y²+z²-2xy-2xz+2yz=9
x²+y²+z²=9-2(yz-xy-xz)=9-2*3=3
答
(x-y-z)^2-2(yz-xy-xz)=x^2+y^2+z^2=3