Question

已知a b c为实数,a+b分之ab=3分之1,b+c分之bc=4分之1,a+c分之 ac=5分之1,求ab+bc+ac

Answer 1

ab/(a+b)=1/3 (a+b)/ab=1/a+1/b=3

bc/(b+c)=1/4 (b+c)/bc=1/c+1/b=4

ac/(a+c)=1/5 (a+c)/ac=1/a+1/c=5

(ab+bc+ac)/abc=1/a+1/b+1/c=(3+4+5)/2=6

∴abc/(ab+bc+ac)=1/6