问题描述: 已知x+y+z=0,x2+y2+z2=1,求xy+yz+xz,x4+y4+z4的解数字为平方和四次方, 1个回答 分类:数学 2014-10-05 问题解答: 我来补答 (x+y+z)^2=[(x+y)+z]^2=(x^2+2xy+y^2)+z^2+2zx+2zy=x^2+y^2+z^2+2xy+2xz+2yz=x^2+y^2+z^2+2(xy+xz+yz)=0x+y+z=0xy + xz+yz= -1/2(xy+xz+yz)^2=x^2y^2+x^2z^2+y^2z^2+2xzy^2+2yzx^2+2xyz^2 =x^2y^2+x^2z^2+y^2z^2 +2xyz(x+y+z)=1/4x^2y^2+x^2z^2+y^2z^2=1/4(x^2+y^2+z^2)^2=x^4+y^4+z^4+2x^2y^2+2x^2z^2+2y^2z^2=1x^4+y^4+z^4= 1/2 展开全文阅读