X+Y+Z=0 a的yz次方＝b的xz次方＝c的xy次方，求abc积

(abc)^(xyz)
=a^(xyz)*b^(xyz)*c^(xyz)
=[a^(yz)]^x *[b^(xz)]^y * [c^(xy)]^z
=[b^(xz)]^x*[b^(xz)]^y*[b^(xz)]^z
=[b^(xz)]^(x+y+z)
=[b^(xz)]^0
=1
所以abc=±1

设a的yz次方＝b的xz次方＝c的xy次方=k.取对数：
yz*loga=zx*logb=xy*logc=logk,
log(abc)=loga+logb+logc
=logk/yz+logk/zx+logk/xy
=(x+y+z)logk/(xyz)
=0,
abc=1.