已知x,y,z满足x+(1⼀y)=4,y+(1⼀z)=1,z+(1⼀x)=7⼀3,则xyz的值为?

2025-05-17 18:25:52
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回答1:

你好

(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

得到: XYZ+1/(XYZ)=2,解得XYZ=1