若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ 的值为-------
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若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ的值为-------若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ的值为-------
若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ 的值为-------
若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ 的值为-------
若实数X.Y.Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,则XYZ 的值为-------
X+1/Y=4
Y+1/Z=1
Z+1/X=7/3
消元后得到二元二次方程组,解得:
X=3/2,Y=2/5,Z=5/3
所以XYZ=1
方程解起来挺烦得,我解了好一会而,要有耐心哦
解法二
(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
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