已知abc为整数且ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5,求abc/(ab+bc+ca)的值
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![已知abc为整数且ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5,求abc/(ab+bc+ca)的值](/uploads/image/z/970589-29-9.jpg?t=%E5%B7%B2%E7%9F%A5abc%E4%B8%BA%E6%95%B4%E6%95%B0%E4%B8%94ab%2F%28a%2Bb%29%3D1%2F3%2Cbc%2F%28b%2Bc%29%3D1%2F4%2Cca%2F%28c%2Ba%29%3D1%2F5%2C%E6%B1%82abc%2F%EF%BC%88ab%2Bbc%2Bca%EF%BC%89%E7%9A%84%E5%80%BC)
已知abc为整数且ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5,求abc/(ab+bc+ca)的值
已知abc为整数且ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5,求abc/(ab+bc+ca)的值
已知abc为整数且ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5,求abc/(ab+bc+ca)的值
取倒数
1/a+1/b=3
1/b+1/c=4
1/c+1/a=5
所以1/a+1/b+1/c=6
所以abc/(ab+bc+ca)=1/6
∵ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5
∴1/a+1/b=3 , 1/b+1/c=4,1/a+1/c=5
∴1/a+1/b+ 1/b+1/c+1/a+1/c=3+4+5=12
1/a+1/b+1/c=6
∴(ab+bc+ca)/abc=6
∴abc/(ab+bc+ca)=1/6
(a+b)/ab=3 ,1/a+1/b=3
(b+c)/bc=4 , 1/b+1/c=4
(c+a)/ca=5 , 1/c+1/a=5
(ab+bc+ca)/abc
=1/a+1/b+1/c
=(3+4+5)/2
=6
则 abc/(ab+bc+ca)=1/6
(b+c)/bc=4,(a+b)/ab=3,(a+c)/=5,
(ab+ac)/abc+(ac+bc)/abc+(ab+bc)/abc=12
(2ab+2ac+2bc)/abc=12
(ab+ac+bc)/=6
abc/(ab+bc+ac)=1/6
取倒数
1/a+1/b=3
1/b+1/c=4
1/c+1/a=5
所以1/a+1/b+1/c=6
abc/(ab+bc+ca)=1/6