Question Number 177763 by lapache last updated on 08/Oct/22 $${Solve}\:{in}\:\mathbb{R}\:{the}\:{system} \\ $$$$\begin{cases}{{x}+{y}={z}}\\{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{{z}}}\end{cases} \\ $$ Commented by mr W last updated on 08/Oct/22 $${no}\:{solution}\:{for}\:{x},{y},{z}\in{R}. \\ $$$${x},\:{y}\:{are}\:{roots}\:{of}\:{t}^{\mathrm{2}}…
Question Number 112217 by mathdave last updated on 06/Sep/20 $${proporsed}\:{by}\:{m}.{n}\:{july}\:\mathrm{1970} \\ $$$${evaluate} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}\mathrm{2}^{{n}} } \\ $$$${solution}\: \\ $$$${recall}\:{that}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{H}_{{n}} {x}^{{n}}…
Question Number 112208 by Khalmohmmad last updated on 06/Sep/20 Commented by Dwaipayan Shikari last updated on 06/Sep/20 $${x}=\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left({from}\:{observation}\right) \\ $$$${y}=\mathrm{4} \\ $$$$ \\…
Question Number 112203 by mathdave last updated on 06/Sep/20 $${proporsed}\:{by}\:{m}.{njuly}\:\mathrm{1970} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}\right)}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$$${solution} \\ $$$${let}\:{I}=\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({x}+\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}\right)}{{x}+\mathrm{1}}{dx}−\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 112193 by ARVIND990 last updated on 06/Sep/20 Commented by mathmax by abdo last updated on 06/Sep/20 $$\mathrm{translate}\:\mathrm{to}\:\mathrm{english}\:\mathrm{or}\:\mathrm{frensh}\:\mathrm{or}\:\mathrm{arabic}…. \\ $$ Terms of Service Privacy…
Question Number 46652 by gunay last updated on 29/Oct/18 $$\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}+\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{2}=\mathrm{3} \\ $$$$\mathrm{could}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Oct/18 $$\left(\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}\right){y}+\left(\mathrm{5}+\frac{\mathrm{1}}{\mathrm{2}}\right){y}=\mathrm{5} \\ $$$${y}\left(\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{5}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{5} \\…
Question Number 177702 by lapache last updated on 08/Oct/22 $${Solve}\:{in}\:\mathbb{C} \\ $$$$\begin{cases}{{x}+{y}={z}}\\{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{{z}}}\end{cases} \\ $$ Answered by Frix last updated on 08/Oct/22 $$\left(\mathrm{1}\right)\:{x}={z}−{y} \\ $$$$\left(\mathrm{2}\right)\:{x}=\frac{{yz}}{{y}−{z}} \\…
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Question Number 112145 by weltr last updated on 06/Sep/20 $$\mathrm{4}^{\mathrm{tan}\:^{\mathrm{2}} {x}} \:+\:\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} {x}}} \:−\:\mathrm{80}\:=\:\mathrm{0} \\ $$ Answered by bemath last updated on 06/Sep/20 $$\mathrm{4}^{\mathrm{tan}\:^{\mathrm{2}} {x}}…
Question Number 177673 by DAVONG last updated on 08/Oct/22 $$\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{a}^{\mathrm{x}} −\mathrm{xlna}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{Help}\:\:\mathrm{please}\:\mathrm{Teacher} \\ $$ Commented by mr W last updated on 08/Oct/22…