（求證哪個(gè)答案正確）某項(xiàng)工程,甲單獨(dú)做所需天數(shù)是乙,丙兩隊(duì)合作所需天數(shù)的A倍；
乙獨(dú)做所需天數(shù)等于甲,丙兩隊(duì)合作所需天數(shù)的B倍；丙獨(dú)做所用天數(shù)等于甲,乙兩隊(duì)和做所需天數(shù)的C倍,求A+1分之1+B+1分之1+C+1分之1得值
設(shè)甲、乙、丙單獨(dú)做各需xyz天
x=a(y+z) a=x/y+z a+1=x+y+z/y+z 1/a+1=y+z/x+y+z
y=b(x+z) b=y/x+z b+1=x+y+z/x+z 1/b+1=x+z/x+y+z
z=c(x+y) c=z/x+y c+1=x+y+z/x+y 1/c+1=x+y/x+y+z
1/(a+z)+1/(b+1)+1/(c+1)
= (y+z)/(x+y+z)+(x+z)/(x+y+z)+(x+y)/(x+y+z)
=2((x+y+z)/(x+y+z)
=2
設(shè)甲、乙、丙單獨(dú)做用的天數(shù)分別為x、y、z天.
那么：a/x = 1/x + 1/y,進(jìn)一步變形可得：1/(a+1) = yz / (xy + yz + xz) ;
同理可得：1/(b+1) = xz / (xy + yz + xz) ; 1/(c+1) = xy / (xy + yz + xz) ;
1/(a+1) ＋1/(b+1)＋ 1/(c+1) =yz / (xy + yz + xz) ＋ xz / (xy + yz + xz) ＋xy / (xy + yz + xz) = 1
應(yīng)該是答案2正確吧