题目

y^2+yz+z^2=a^2,z^2+zx+x^2=b^2,x^2+xy+y^2=c^2,yz+zx+xy=0.证明:(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0

提问时间：2021-03-06

答案

y^2+yz+z^2=a^2,yz≥0
z^2+zx+x^2=b^2,zx≥0
x^2+xy+y^2=c^2,xy≥0
yz+zx+xy=0,x＝y＝z＝0
(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 y^2+yz+z^2=a^2,yz≥0
z^2+zx+x^2=b^2,zx≥0
x^2+xy+y^2=c^2,xy≥0
yz+zx+xy=0,x＝y＝z＝0
(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 y^2+yz+z^2=a^2,yz≥0
z^2+zx+x^2=b^2,zx≥0
x^2+xy+y^2=c^2,xy≥0
yz+zx+xy=0,x＝y＝z＝0
(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0 y^2+yz+z^2=a^2,yz≥0
z^2+zx+x^2=b^2,zx≥0
x^2+xy+y^2=c^2,xy≥0
yz+zx+xy=0,x＝y＝z＝0
(a+b+c)(a+b-c)(a-b+c)(a-b-c)=0