Question

若abc均为正数,且xyz不等于1,a'xb'yc'z=a'yb'zc'x=a'zb'xc'y=1.求x.y.z之间的关系.

Answer 1

(a^x * a^y * a^z)*(b^x * b^y * b^z)*(c^x * c^y * c^z)=(abc)^(x+y+z)=(a^x * b^y * c^z) * (a^y * b^z * c^x) * (a^z * b^x * c^y)=1*1*1=1(abc)^(x+y+z)=1x+y+z = 0 或者 当abc=1时 xyz为不为1的数