已知x^2+y^2+z^2=8,xy+yz+xz=4.则(x+y+z)^2=

问题描述:

已知x^2+y^2+z^2=8,xy+yz+xz=4.则(x+y+z)^2=

(x+y+z)^2
=(x+y)²+z²+2(x+y)z
=x²+y²+2xy+z²+2xz+2yz
=x²+y²+z²+2(xy+yz+xz)
=8+2*4
=16