Question

已知abc≠0,x、y、z为整数,且x+y+z=0,a的yz次方等于b的xz次方等于c的xy次方,求abc的值

Answer 1

(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