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

$$\mathrm{Given}\{\begin{array}{l}\mathrm{a}+\mathrm{b}=5\mathrm{ab}\\ \mathrm{b}+\mathrm{c}=7\mathrm{bc}\\ \mathrm{c}+\mathrm{a}=6\mathrm{ac}\end{array}$$$$\mathrm{where}\mathrm{a},\mathrm{b},\mathrm{c}\ne 0.$$$$\mathrm{Find}\mathrm{abc}$$

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

$$\frac{1}{a}+\frac{1}{b}=5\iff A+B=5$$$$\frac{1}{b}+\frac{1}{c}=7\iff B+C=7$$$$\frac{1}{a}+\frac{1}{c}=6\iff A+C=6$$$$\Rightarrow A=2B=3C=4$$$$\Rightarrow abc=\frac{1}{ABC}=\frac{1}{24}$$

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

$$Nicesir!$$

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