Question Number 158884 by akolade last updated on 10/Nov/21 Answered by ghimisi last updated on 10/Nov/21 $${log}_{\mathrm{3}} \left({a}+\mathrm{1}\right)={log}_{\mathrm{4}} \left({a}+\mathrm{8}\right)={t}\Rightarrow \\ $$$${a}+\mathrm{1}=\mathrm{3}^{{t}} \\ $$$${a}+\mathrm{8}=\mathrm{4}^{{t}} \Rightarrow\mathrm{4}^{{t}} −\mathrm{3}^{{t}}…
Question Number 158883 by akolade last updated on 10/Nov/21 Commented by Rasheed.Sindhi last updated on 10/Nov/21 $$\left(\underset{{a}} {\underbrace{\sqrt{\mathrm{3}}\:+{x}}}\right)^{\mathrm{12}} +\left(\underset{{b}} {\underbrace{\sqrt{\mathrm{3}}\:−{x}}}\right)^{\mathrm{12}} =\mathrm{172928};{x}=? \\ $$$${a}+{b}=\mathrm{2}\sqrt{\mathrm{3}}\:;{ab}=\mathrm{3}−{x}^{\mathrm{2}} ={y}\:\left({say}\right) \\…
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Question Number 93315 by Shakhzod last updated on 12/May/20 $${If}\:\:{n}>=\mathrm{2}\:\:{and}\:{n}\subset\mathbb{N}\:. \\ $$$${prove}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+…\frac{\mathrm{1}}{{n}^{\mathrm{2}} }<={n}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93304 by Shakhzod last updated on 12/May/20 $$\int\sqrt{\mathrm{tan}\:\left({x}\right)}{dx}\:{Who}\:{can}\:{solve}\:{this}\:{problem}? \\ $$ Commented by john santu last updated on 12/May/20 $$=\:−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:}\mathrm{tanh}\:^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}+\sqrt{\mathrm{cot}\:\mathrm{x}}}{\:\sqrt{\mathrm{2}}}\right)\:+\: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{cot}\:\mathrm{x}}}{\:\sqrt{\mathrm{2}}}\right)+\mathrm{c}\:\:…
Question Number 158829 by MathsFan last updated on 09/Nov/21 $$\:{The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:{are}\:\mathrm{2}\alpha+\beta\:{and} \\ $$$$\:\alpha+\mathrm{2}\beta.\:{Calculate}\:{the}\:{values}\:{of} \\ $$$$\:{p}\:{and}\:{q} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 93284 by naka3546 last updated on 12/May/20 Commented by mr W last updated on 12/May/20 $${no}\:{unique}\:{solution}! \\ $$$$\left[{EFGH}\right]\geqslant\mathrm{2}\left[{ABCD}\right]=\mathrm{4}{M} \\ $$ Commented by mr…
Question Number 158794 by SANOGO last updated on 08/Nov/21 $${montrer}\:{que}\:\mathrm{7}\:{divise} \\ $$$$\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on 09/Nov/21 $${We}'{ll}\:\:{determine}\:{remainders}…
Question Number 27718 by mondodotto@gmail.com last updated on 13/Jan/18 Answered by prakash jain last updated on 13/Jan/18 $$\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:\right)^{{x}} ={a} \\ $$$$\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:\right)^{{x}} =\frac{\mathrm{1}}{{a}} \\ $$$${a}+\frac{\mathrm{1}}{{a}}=\mathrm{4}\Rightarrow{a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{1}=\mathrm{0}…