x/a+y/b+z/c=1,
平方得x^2/a^2+y^2/b^2+z^2/c^2+2[xy/(ab)+yz/(bc)+zx/(ca)]=1,①
a/x+b/y+c/z=0,
两边都乘以xyz/(abc),得yz/(bc)+zx/(ca)+xy/(ab)=0,②
①-②*2,得x^2/a^2+y^2/b^2+z^2/c^2=1.
x/a+y/b+z/c=1,
平方得x^2/a^2+y^2/b^2+z^2/c^2+2[xy/(ab)+yz/(bc)+zx/(ca)]=1,①
a/x+b/y+c/z=0,
两边都乘以xyz/(abc),得yz/(bc)+zx/(ca)+xy/(ab)=0,②
①-②*2,得x^2/a^2+y^2/b^2+z^2/c^2=1.