X+Y+Z=0 a的yz次方＝b的xz次方＝c的xy次方,求abc积

题目

X+Y+Z=0 a的yz次方＝b的xz次方＝c的xy次方,求abc积

答案

(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