Given-a-b-5ab-b-c-7bc-c-a-6ac-where-a-b-c-0-Find-abc-

Question Number 134912 by bramlexs22 last updated on 08/Mar/21

Given {\begin{cases} a + b = 5 ab \\ b + c = 7 bc \\ c + a = 6 ac \end{cases}

where a, b, c \neq 0 .

Find abc

Answered by Ñï= last updated on 08/Mar/21

\frac{1}{a} + \frac{1}{b} = 5 \Leftrightarrow A + B = 5

\frac{1}{b} + \frac{1}{c} = 7 \Leftrightarrow B + C = 7

\frac{1}{a} + \frac{1}{c} = 6 \Leftrightarrow A + C = 6

\Rightarrow A = 2 B = 3 C = 4

\Rightarrow a b c = \frac{1}{A B C} = \frac{1}{24}

Commented by Rasheed.Sindhi last updated on 10/Mar/21

N i c e s i r!