1.已知:x^2+y^2+z^2=xy+yz+xz 求证:x=y=z

2025-02-25 13:53:40
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回答1:

x^2+y^2+z^2=xy+yz+xz
2(x^2+y^2+z^2)=2(xy+yz+xz)
x^2+y^2-2xy+x^2+z^2-2xz+y^2+z^2-2yz=0
(x-y)^2+(y-z)^2+(x-z)^2=0
x-y=0 y-z=0 x-z=0
x=y=z