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Determine-a-triplet-a-b-c-of-real-numbers-with-a-relation-a-1-b-1-c-1-and-satisfying-the-following-conditions-a-b-gt-c-b-c-gt-a-c-a-gt-b-




Question Number 4216 by Rasheed Soomro last updated on 02/Jan/16
Determine a triplet (a,b,c) of real numbers   with a relation a^(−1) +b^(−1) =c^(−1) and  satisfying the  following conditions        a+b>c ∧ b+c>a ∧ c+a>b .
$$\boldsymbol{\mathrm{D}}\mathrm{etermine}\:\mathrm{a}\:\mathrm{triplet}\:\left(\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\right)\:\mathrm{of}\:\mathrm{real}\:\mathrm{numbers}\: \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{relation}\:\boldsymbol{\mathrm{a}}^{−\mathrm{1}} +\boldsymbol{\mathrm{b}}^{−\mathrm{1}} =\boldsymbol{\mathrm{c}}^{−\mathrm{1}} \mathrm{and}\:\:\mathrm{satisfying}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{conditions} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}>\boldsymbol{\mathrm{c}}\:\wedge\:\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}>\boldsymbol{\mathrm{a}}\:\wedge\:\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}>\boldsymbol{\mathrm{b}}\:. \\ $$

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