Question Number 173993 by AgniMath last updated on 22/Jul/22 Answered by som(math1967) last updated on 22/Jul/22 $$\:{xy}+{yz}+{zx}+\mathrm{2}{xyz} \\ $$$$=\frac{{ab}}{\left({b}+{c}\right)\left({c}+{a}\right)}\:+\frac{{bc}}{\left({c}+{a}\right)\left({a}+{b}\right)} \\ $$$$\:\:+\frac{{ca}}{\left({a}+{b}\right)\left({b}+{c}\right)}+\frac{\mathrm{2}{abc}}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)} \\ $$$$=\frac{{ab}\left({a}+{b}\right)+{bc}\left({b}+{c}\right)+{ca}\left({c}+{a}\right)+\mathrm{2}{abc}}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)} \\ $$$$=\frac{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}\:\:\:\:\:\bigstar…
Question Number 108456 by Khalmohmmad last updated on 17/Aug/20 Commented by Rizwankhan last updated on 17/Aug/20 $${how}\:{did}\:{you}\:{added}\:{this}\:{page}\:{sir}? \\ $$ Answered by bemath last updated on…
Question Number 42908 by naka3546 last updated on 04/Sep/18 $${Solve}\: \\ $$$$\:\:\:\:\:\mathrm{21}^{{a}} \:+\:\mathrm{28}^{{b}} \:\:=\:\:\mathrm{35}^{{c}} \\ $$$${if} \\ $$$${a},\:{b},\:\:{and}\:\:{c}\:\:{are}\:\:{positive}\:\:{integers}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 42909 by naka3546 last updated on 04/Sep/18 $${How}\:\:{many}\:\:{pairs}\:{of}\:\:\left({a},\:{b},\:{c},\:{d}\right)\:\:{so}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{a}!\:+\:\:{b}!\:\:+\:\:{c}!\:\:=\:\:{d}! \\ $$$${which}\:\:\:{a},\:{b},\:{c},\:{d}\:\:\in\:\:{positive}\:\:{integers}\:. \\ $$ Answered by MJS last updated on 04/Sep/18 $$\mathrm{only}\:\mathrm{1}:\:\mathrm{2}!+\mathrm{2}!+\mathrm{2}!=\mathrm{3}! \\…
Question Number 108420 by mathdave last updated on 16/Aug/20 Answered by prakash jain last updated on 18/Sep/20 $$−−−−−−−−−−−−−−−− \\ $$$$\mathrm{12}+\mathrm{3}=\mathrm{15}\:\mathrm{dashes} \\ $$$$\mathrm{select}\:\mathrm{3}\:\mathrm{dashes}\:\mathrm{and}\:\mathrm{change}\:\mathrm{them}\:\mathrm{to} \\ $$$$\mathrm{bar}\:\mathrm{it}\:\mathrm{will}\:\mathrm{create}\:\mathrm{four}\:\mathrm{partions} \\…
Question Number 108417 by mathdave last updated on 16/Aug/20 Answered by Aziztisffola last updated on 16/Aug/20 $$\mathrm{t}=\mathrm{2x}\:\Rightarrow\mathrm{dt}=\mathrm{2dx} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{2x}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{1}}\:\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{t}}{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}\:\mathrm{dt}…
Question Number 108416 by mathdave last updated on 16/Aug/20 Answered by mathmax by abdo last updated on 16/Aug/20 $$\mathrm{I}\:=\int\:\mathrm{ln}\left(\sqrt{\mathrm{1}+\mathrm{x}}+\sqrt{\mathrm{1}−\mathrm{x}}\right)\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{cos}\left(\mathrm{2t}\right)\:\Rightarrow \\ $$$$\mathrm{I}\:=\int\:\mathrm{ln}\left(\sqrt{\mathrm{2cos}^{\mathrm{2}} \mathrm{t}}\:+\sqrt{\mathrm{2sin}^{\mathrm{2}} \mathrm{t}}\right)\left(−\mathrm{2sin}\left(\mathrm{2t}\right)\:\mathrm{dt}\right. \\ $$$$=−\mathrm{2}\:\int\:\mathrm{ln}\left(\sqrt{\mathrm{2}}\left(\mathrm{cost}\:+\mathrm{sint}\right)\mathrm{sin}\left(\mathrm{2t}\right)\mathrm{dt}\right.…
Question Number 108415 by mathdave last updated on 16/Aug/20 Commented by bobhans last updated on 17/Aug/20 $$\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)}\:=\:\frac{{p}}{{n}}+\frac{{q}}{{n}+\mathrm{2}}+\frac{{r}}{{n}+\mathrm{4}} \\ $$$$\mathrm{1}={p}\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)+{qn}\left({n}+\mathrm{4}\right)+{rn}\left({n}+\mathrm{2}\right) \\ $$$${n}=\mathrm{0}\Rightarrow\mathrm{1}=\mathrm{8}{p}\rightarrow{p}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${n}=−\mathrm{2}\Rightarrow\mathrm{1}=−\mathrm{4}{q}\rightarrow{q}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${n}=−\mathrm{4}\Rightarrow\mathrm{1}=\mathrm{8}{r}\rightarrow{r}=\frac{\mathrm{1}}{\mathrm{8}}…
Question Number 108413 by Yusufa last updated on 16/Aug/20 $$\mathrm{228}{x}=\mathrm{87}\:{find}\:{x} \\ $$ Answered by Aziztisffola last updated on 16/Aug/20 $${x}=\frac{\mathrm{87}}{\mathrm{288}} \\ $$ Commented by Sarah85…
Question Number 42861 by mondodotto@gmail.com last updated on 03/Sep/18 $$\mathrm{14}\boldsymbol{\div}\mathrm{2}\left(\mathrm{3}+\mathrm{4}\right)=? \\ $$ Answered by MJS last updated on 03/Sep/18 $$\mathrm{brackets}\:\mathrm{first} \\ $$$$×/\:\mathrm{before}\:+− \\ $$$$\mathrm{14}/\mathrm{2}×\left(\mathrm{3}+\mathrm{4}\right)=\mathrm{14}/\mathrm{2}×\mathrm{7}=\mathrm{49} \\…