Question Number 200942 by Mingma last updated on 26/Nov/23 Answered by witcher3 last updated on 26/Nov/23 $$\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{2}} }\geqslant\mathrm{3}\left(\mathrm{abc}\right)^{−\frac{\mathrm{2}}{\mathrm{3}}} \:\:\mathrm{AM}−\mathrm{GM} \\ $$$$\mathrm{ab}+\mathrm{bc}+\mathrm{ac}\geqslant\Leftrightarrow \\ $$$$\mathrm{abc}\left(\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}+\frac{\mathrm{1}}{\mathrm{c}}\right)\geqslant\mathrm{1}…
Question Number 200937 by Mingma last updated on 26/Nov/23 Answered by MM42 last updated on 26/Nov/23 $$\frac{\mathrm{25}\sqrt{\mathrm{2}}}{\mathrm{4}}\pi \\ $$ Commented by Mingma last updated on…
Question Number 200931 by Spillover last updated on 26/Nov/23 $$\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{45}}+\frac{\mathrm{1}}{\mathrm{63}}+\frac{\mathrm{1}}{\mathrm{84}}+…\infty=? \\ $$$$ \\ $$ Answered by MM42 last updated on 26/Nov/23 $${s}_{{n}} =\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\right)=\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}−\frac{\mathrm{1}}{{n}+\mathrm{2}}\right)\:\: \\ $$$$\Rightarrow{s}_{{n}}…
Question Number 200858 by Abdullahrussell last updated on 25/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200877 by mathlove last updated on 25/Nov/23 Commented by mr W last updated on 25/Nov/23 $${we}\:{know}\:{a}^{\mathrm{log}_{{a}} \:{b}} ={b},\:{so}\:{we}\:{can}\:“{see}'' \\ $$$${that}\:{x}=\mathrm{3}\:{is}\:{a}\:{root}. \\ $$ Commented…
Question Number 200795 by mathlove last updated on 23/Nov/23 $$\underset{{x}\rightarrow{sin}\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{cosx}}=? \\ $$ Answered by witcher3 last updated on 23/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{is}\:\:\mathrm{defined}\:\mathrm{in}\:\mathrm{sin}\left(\mathrm{1}\right) \\ $$$$…
Question Number 200788 by hardmath last updated on 23/Nov/23 $$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 23/Nov/23 $${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}}…
Question Number 200768 by Abdullahrussell last updated on 23/Nov/23 Answered by Frix last updated on 23/Nov/23 $$\mathrm{Wrong}. \\ $$$$\mathrm{2}^{\mathrm{11}} −\mathrm{1}=\mathrm{2047}=\mathrm{23}×\mathrm{89} \\ $$ Answered by BaliramKumar…
Question Number 200696 by Bayat last updated on 22/Nov/23 Answered by aleks041103 last updated on 22/Nov/23 $$\left(\mathrm{2}^{{x}} −\mathrm{3}^{{x}} \right)^{\mathrm{2}} =\mathrm{4}^{{x}} +\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{6}^{{x}} =\mathrm{6}^{{x}} −\mathrm{9}^{{x}} \\…
Question Number 200739 by mr W last updated on 22/Nov/23 $${solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−\mathrm{2}}+\mathrm{2}=\mathrm{0} \\ $$ Commented by Frix last updated on 23/Nov/23 $${x}^{\mathrm{3}} −{px}+{q}=\mathrm{0}…