X加Y分之一等于4 Y加Z分之一等于1 Z加X分之一等于三分之七 数学题 求XYZ值

(X+1/Y)(Z+1/X)(Y+1/Z)
=XYZ+1/(XYZ)+X+Y+Z+1/X+1/Y+1/Z
=XYZ+1/(XYZ)+4+1+7/3=4*1*7/3
=XYZ+1/(XYZ)+22/3=28/3
=XYZ+1/(XYZ)=2
解得XYZ=1