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Question Number 43706 by Tawa1 last updated on 14/Sep/18

If pqr = 1 Hence evaluate: (1/(1 + e + f^(−1) )) + (1/(1 + f + g^(−1) )) + (1/(1 + g + e^(−1) ))

$$\mathrm{If}\:\:\mathrm{pqr}\:=\:\mathrm{1} \\ $$$$\mathrm{Hence}\:\mathrm{evaluate}:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{e}\:+\:\mathrm{f}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{f}\:+\:\mathrm{g}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{g}\:+\:\mathrm{e}^{−\mathrm{1}} } \\ $$

Commented by Joel578 last updated on 14/Sep/18

p,q,r and e,f,g ?

$${p},{q},{r}\:\mathrm{and}\:{e},{f},{g}\:? \\ $$

Commented by Tawa1 last updated on 14/Sep/18

No value is given sir. That is just the question

$$\mathrm{No}\:\mathrm{value}\:\mathrm{is}\:\mathrm{given}\:\mathrm{sir}.\:\mathrm{That}\:\mathrm{is}\:\mathrm{just}\:\mathrm{the}\:\mathrm{question} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 14/Sep/18

(1/(1+p+q^(−1) ))+(1/(1+q+r^(−1) ))+(1/(1+r+p^(−1) )) (q/(q+pq+1))+(1/(1+q+pq))+(1/(1+(1/(pq))+(1/p))) (q/(q+pq+1))+(1/(1+q+pq))+((pq)/(pq+1+q)) =((q+1+pq)/(q+pq+1))=1

$$\frac{\mathrm{1}}{\mathrm{1}+{p}+{q}^{−\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{1}+{q}+{r}^{−\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{1}+{r}+{p}^{−\mathrm{1}} } \\ $$$$\frac{{q}}{{q}+{pq}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{1}+{q}+{pq}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{{pq}}+\frac{\mathrm{1}}{{p}}} \\ $$$$\frac{{q}}{{q}+{pq}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{1}+{q}+{pq}}+\frac{{pq}}{{pq}+\mathrm{1}+{q}} \\ $$$$=\frac{{q}+\mathrm{1}+{pq}}{{q}+{pq}+\mathrm{1}}=\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Commented by Tawa1 last updated on 14/Sep/18

wow, God bless you sir

$$\mathrm{wow},\:\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by Meritguide1234 last updated on 15/Sep/18

you have solved different problem

$${you}\:{have}\:{solved}\:{different}\:{problem} \\ $$

Commented by Tawa1 last updated on 14/Sep/18

I understand. the solution is correct. God bless mr tanmay

$$\mathrm{I}\:\mathrm{understand}.\:\mathrm{the}\:\mathrm{solution}\:\mathrm{is}\:\mathrm{correct}.\:\:\mathrm{God}\:\mathrm{bless}\:\mathrm{mr}\:\mathrm{tanmay} \\ $$

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