已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15求abc/ab+bc+ac的值结果为60/31

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已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15求abc/ab+bc+ac的值结果为60/31

已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15求abc/ab+bc+ac的值结果为60/31
已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15求abc/ab+bc+ac的值
结果为60/31

已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15求abc/ab+bc+ac的值结果为60/31
(ab+bc+ac)/abc=1/a+1/b+1/c=1/2(1/a+1/b+1/a+1/c+1/b+1/c)=1/2(1/6+1/9+1/15)=31/180,固原式=180/31

1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15
加起来
2(1/a+1/b+1/c)=31/90
1/a+1/b+1/c=31/180
(ab+bc+ca)/abc
=ab/abc+bc/abc+ca/abc
=1/c+1/a+1/b
=31/180
所以abc/(ab+bc+ca)=180/31