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Question Number 36061 by Raj Singh last updated on 28/May/18

Commented by Rasheed.Sindhi last updated on 28/May/18

$$\mathcal{N}otrelatedtotheabovequestion.$$$$\mathcal{D}\mathrm{ear}\mathrm{Abu}\mathrm{behi},$$$$\mathcal{I}{}^{\prime }\mathrm{ve}\mathrm{discovered}\mathrm{relation}\mathrm{between}\mathrm{your}$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{And}\mathrm{now}\mathrm{I}\mathrm{know}\mathrm{that}{\mathrm{you}}^{\prime }\mathrm{ve}\mathrm{a}\mathrm{solution}$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$35844).\mathrm{But}\mathrm{wait}...$$$$\mathrm{Let}\mathrm{Mr}\mathrm{tanmay}\mathrm{\&}\mathrm{S}@\mathrm{ty}@\mathrm{m}\mathrm{complete}$$$$\mathrm{their}\mathrm{trials}.$$$$\mathcal{BTW}$$$$\mathcal{D}\mathrm{o}\mathrm{you}\mathrm{like}\mathrm{to}\mathrm{be}\mathrm{called}\mathrm{Abu}\mathrm{behi}\mathrm{by}\mathrm{me}?$$$$\mathrm{If}\mathrm{not}\mathrm{I}\mathrm{will}\mathrm{ever}\mathrm{call}\mathrm{you}\mathrm{Mr}\mathrm{Behi}.$$

Commented by behi83417@gmail.com last updated on 28/May/18

$$dearmrRasheed!youarerightand$$$$youarewelcome.$$

Answered by math1967 last updated on 28/May/18

$$Ithink$$$$L.H.S\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}$$$$=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}$$$$=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}$$$$[\because abc=1,\therefore \frac{1}{c}=abandc=\frac{1}{ab}]$$$$=\frac{b}{b+ab+1}+\frac{1}{b+ab+1}+\frac{ab}{ab+1+b}$$$$=\frac{b+1+ab}{b+1+ab}=1=R.H.S$$$$AmIcorrect?$$

Commented by Rasheed.Sindhi last updated on 28/May/18

$${\mathrm{e}}^{\mathrm{x}}\mathrm{cellent}!$$

Commented by math1967 last updated on 29/May/18

$$Mypleasure$$

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