Question

ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5求a、b、c的值

Answer 1

ab/(a+b)=1/3
bc/(b+c)=1/4
ca/(c+a)=1/5
即：
(a+b)/(ab)=3
(b+c)/(bc)=4
(c+a)/(ca)=5
即：
1/a+1/b=3 ......(1)
1/b+1/c=4 ......(2)
1/c+1/a=5 ......(3)
(1)+(2)+(3)得：
2(1/a+1/b+1/c) = 3+4+5 = 12
1/a+1/b+1/c = 6 ......(4)
(4)-(2)得：1/a=2，a=1/2
(4)-(3)得：1/b=1，b=1
(4)-(1)得：1/c=3，c=1/3

Answer 2

因为ab/(a+b)=1/3,bc/(b+c)=1/4,ca/(c+a)=1/5
所以(a+b)/ab=3,(b+c)/bc=4,(c+a)/ca=5
所以(1/a+1/b+1/c)*2=12
所以1/a+1/b+1/c＝6
所以a=1/2,b=1,c=1/3

Answer 3

(a+b)/ab = 3 即 1/b + 1/a =3 (1)
同理 1/b + 1/c =4 (2)
1/a + 1/c =5 (3)
(3) -(2) 1/a - 1/b =1 (4)
(1) + (4) 2/a = 4 a =1/2
代入解得 b =1 c =1/3

Answer 4

每一项两边同时取倒数 解方程组易得a=1/2 b=1 c=1/3

Answer 5

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