> 数学 >
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
人气:371 ℃ 时间:2020-05-08 13:36:08
解答
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
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版