1/x+1/y=1/61/y+1/z=1/10(1/x+1/z)*5=2/3
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1/x+1/y=1/61/y+1/z=1/10(1/x+1/z)*5=2/3
1/x+1/y=1/6
1/y+1/z=1/10
(1/x+1/z)*5=2/3
1/x+1/y=1/61/y+1/z=1/10(1/x+1/z)*5=2/3
1/x+1/y=1/6(1)
1/y+1/z=1/10(2)
(1/x+1/z)*5=2/3(3)
(3)式两边除以5得:1/x+1/z=2/15(4)
(1)-(2)得1/x-1/z=1/15(5)
(4)+(5)得1/x=1/10
解得x=10
y=15
z=30
第三个式子得:1/x+1/z=2/15 ⑷
三个式子相加:2(1/x+1/y+1/z)=1/6+1/10+2/15=2/5;所以:1/x+1/y+1/z=1/5 ⑸
再⑸-⑴得1/z=1/5-1/6=1/30,则z=30
再⑸-⑵得1/x=1/5-1/10=1/10,则x=10
最后得y=15
1/X+1/Y-(1/Y+1/Z)=1/6-1/10
1/X-1/Z=1/15
(1/X-1/Z)*5+(1/X+1/Z)*5=(1/15)*5+2/3
X=10
Y=15
Z=30
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