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Category: Algebra

Question-69411

Question Number 69411 by ahmadshah last updated on 23/Sep/19 Commented by Prithwish sen last updated on 23/Sep/19 $$\mathrm{h}+\mathrm{t}−\mathrm{c}=\mathrm{85}….\left(\mathrm{i}\right) \\ $$$$\mathrm{h}+\mathrm{t}+\mathrm{c}=\mathrm{155}…\left(\mathrm{ii}\right) \\ $$$$\left(\mathrm{ii}\right)−\left(\mathrm{i}\right)\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{get}}\:\:\boldsymbol{\mathrm{c}}=\:\mathrm{35}\:\boldsymbol{\mathrm{cm}}\:\: \\ $$ Terms…

Question-69413

Question Number 69413 by ahmadshah last updated on 23/Sep/19 Commented by kaivan.ahmadi last updated on 23/Sep/19 $$\frac{\left(\mathrm{5}×\frac{\mathrm{4}}{\mathrm{5}}\right)^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} }=\frac{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} ×\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}}…

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 $$\mathrm{Given}\:\begin{cases}{\mathrm{a}+\mathrm{b}=\mathrm{5ab}}\\{\mathrm{b}+\mathrm{c}=\mathrm{7bc}}\\{\mathrm{c}+\mathrm{a}=\mathrm{6ac}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\neq\:\mathrm{0}. \\ $$$$\mathrm{Find}\:\mathrm{abc} \\ $$ Answered by Ñï= last updated on 08/Mar/21 $$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}=\mathrm{5}\Leftrightarrow{A}+{B}=\mathrm{5} \\…

Show-that-a-b-R-a-b-1-3-b-a-1-3-2-a-b-1-a-1-b-1-3-

Question Number 3832 by Yozzii last updated on 21/Dec/15 $${Show}\:{that},\:\forall{a},{b}\in\mathbb{R}^{+} , \\ $$$$\:\left(\frac{{a}}{{b}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{b}}{{a}}\right)^{\mathrm{1}/\mathrm{3}} \leqslant\left\{\mathrm{2}\left({a}+{b}\right)\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\right\}^{\mathrm{1}/\mathrm{3}} . \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…

n-0-2n-1-2-2n-1-

Question Number 3807 by Rasheed Soomro last updated on 21/Dec/15 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}^{\mathrm{2}{n}+\mathrm{1}} }=? \\ $$ Answered by Yozzii last updated on 21/Dec/15 $${s}=\underset{{n}=\mathrm{0}} {\overset{\infty}…