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Question Number 185536 by mathlove last updated on 23/Jan/23 $${x}^{\mathrm{4}} +{x}^{{ln}\mathrm{5}} =\mathrm{19} \\ $$$${x}^{{lnx}} +{ln}^{\mathrm{2}} {x}=\mathrm{4} \\ $$$${x}=? \\ $$ Commented by Frix last updated…
Question Number 54466 by 05051993 last updated on 04/Feb/19 $$\frac{\mathrm{6}+\sqrt{\left(\mathrm{6}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{10}\right)}}{\mathrm{2}} \\ $$$$ \\ $$ Commented by Tawa1 last updated on 04/Feb/19 $$=\:\frac{\mathrm{6}\:+\:\sqrt{\mathrm{36}\:−\:\mathrm{40}}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{6}\:+\:\sqrt{−\:\mathrm{4}}}{\mathrm{2}}…
Question Number 119996 by behi83417@gmail.com last updated on 28/Oct/20 $$\begin{cases}{\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{2}} =\boldsymbol{{a}}}\\{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{3}} =\boldsymbol{{b}}}\end{cases}\:\:\:\left[\boldsymbol{{solve}}\:\boldsymbol{{for}}:\mathrm{x},\mathrm{y},\mathrm{a}\neq\mathrm{b}\in\boldsymbol{\mathrm{R}}\right] \\ $$ Answered by TANMAY PANACEA last updated on 28/Oct/20 $${x}^{\mathrm{6}}…
Question Number 119997 by behi83417@gmail.com last updated on 28/Oct/20 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\mathrm{a}\in\boldsymbol{\mathrm{R}}. \\ $$$$\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\boldsymbol{{a}}^{\mathrm{2}} }+\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{{ax}}+\boldsymbol{{a}}^{\mathrm{2}} }=\mathrm{1} \\ $$ Answered by Lordose last updated on 28/Oct/20…
Question Number 185529 by Rupesh123 last updated on 23/Jan/23 Answered by Frix last updated on 23/Jan/23 $${x}=\frac{\mathrm{1}}{{a}}\wedge{y}=\frac{\mathrm{1}}{{b}}\wedge{z}=\frac{\mathrm{1}}{{c}}\:\Rightarrow \\ $$$$\left({x}+{y}+{z}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \\ $$$$\mathrm{2}\left({xy}+{yz}+{zx}\right)=\mathrm{0}\:\Rightarrow \\…
Question Number 185522 by Mingma last updated on 23/Jan/23 Commented by Frix last updated on 23/Jan/23 $$\mathrm{This}\:\mathrm{only}\:\mathrm{requires} \\ $$$${r}=\frac{{D}}{\mathrm{2}\left({a}+{b}+{c}\right)} \\ $$$${R}=\frac{{abc}}{{D}} \\ $$$${D}=\sqrt{\left({a}+{b}+{c}\right)\left({b}+{c}−{a}\right)\left({a}+{c}−{b}\right)\left({a}+{b}−{c}\right)} \\ $$…
Question Number 185515 by HeferH last updated on 23/Jan/23 $$\:{At}\:{a}\:{party}\:{with}\:“{m}''\:{people},\:{a}\:{lady}\:{dances} \\ $$$$\:{with}\:{p}\:{gentlemen},\:{the}\:{second}\:{with}\:{p}\:+\:\mathrm{1},\: \\ $$$$\:{the}\:{third}\:{one}\:{with}\:{p}\:+\:\mathrm{2},\:{and}\:{so}\:{on}\:{until}\:{the} \\ $$$$\:{last}\:{one}\:{dances}\:{with}\:{all}\:{the}\:{gentlemen},\: \\ $$$$\:{find}\:{the}\:{number}\:{of}\:{ladies}\:{who}\:{attended}\:{the} \\ $$$$\:{party}\:{in}\:{terms}\:{of}\:“{m}''{and}\:“{p}''. \\ $$ Answered by manxsol…
Question Number 119979 by huotpat last updated on 28/Oct/20 Commented by huotpat last updated on 28/Oct/20 $${N}\:{when}\:{n}\rightarrow+\infty\:{is}\:{not}\:{x}\rightarrow+\infty \\ $$ Answered by mathmax by abdo last…
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