Question Number 91439 by Cynosure last updated on 30/Apr/20 $${solve}\:\mathrm{2}{x}^{\mathrm{99}} +\mathrm{3}{x}^{\mathrm{98}} +\mathrm{2}{x}^{\mathrm{97}} +\mathrm{3}{x}^{\mathrm{96}} +…..\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:{in}\:\mathbb{R} \\ $$ Commented by Cynosure last updated on 30/Apr/20 $${pls}\:{i}\:{need}\:{answer} \\…
Question Number 156419 by cortano last updated on 11/Oct/21 $$\mathrm{x}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{number}\: \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{check}\:\mathrm{if}\:\mathrm{Q}=\sqrt[{\mathrm{3}}]{\left(\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} −\mathrm{x}^{\mathrm{4}} \right.} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number} \\ $$ Commented by mr W last updated on…
Question Number 90698 by jagoll last updated on 25/Apr/20 $${how}\:{many}\:{solution}\:{the}\:{equation} \\ $$$$\lfloor\:{x}\:\rfloor\:+\mathrm{2016}.\:\left\{{x}\right\}\:=\:\mathrm{38}? \\ $$ Commented by mr W last updated on 25/Apr/20 $${in}\:{general} \\ $$$$\lfloor\:{x}\:\rfloor\:+{n}\left\{{x}\right\}\:=\:{m}…
Question Number 25152 by tawa tawa last updated on 05/Dec/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{real}\:\mathrm{part}\:\mathrm{and}\:\mathrm{imaginary}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number}:\:\:\:\:\mathrm{z}\:=\:\left(\mathrm{1}\:+\:\mathrm{i}\right)^{\mathrm{i}} \\ $$ Commented by tawa tawa last updated on 05/Dec/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered…
Question Number 156201 by VIDDD last updated on 09/Oct/21 $$\:\:{A}=\left[\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{2}} } \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{3}} } \centerdot\centerdot\centerdot\centerdot\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{n}} } }}}}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$ Commented by talminator2856791 last updated on…
Question Number 156126 by VIDDD last updated on 08/Oct/21 $$\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{5}}=…?\:\:\mathrm{with}\:\mathrm{solution}\:\mathrm{pls} \\ $$ Commented by cortano last updated on 08/Oct/21 $$\frac{\pi}{\mathrm{5}}=\mathrm{36}°\:\Rightarrow\mathrm{cos}\:\mathrm{72}°=\mathrm{2cos}\:\mathrm{36}°−\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{36}°=\sqrt{\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{72}°}{\mathrm{2}}}=\sqrt{\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{18}°}{\mathrm{2}}} \\ $$ Answered…
Question Number 24944 by soufiane zarik last updated on 29/Nov/17 Commented by prakash jain last updated on 30/Nov/17 $${x}={n}+{f}\:\:\mathrm{0}\leqslant{f}<\mathrm{1},\:{n}\in\mathbb{Z},{n}\geqslant\mathrm{0} \\ $$$$\left[\left({n}+{f}\right)^{\mathrm{2}} \right]=\left[{n}+{f}\right]^{\mathrm{2}} \\ $$$$\Rightarrow\left[{n}^{\mathrm{2}} +\mathrm{2}{nf}+{f}^{\mathrm{2}}…
Question Number 90470 by Asif Hypothesis last updated on 23/Apr/20 $${For}\:{any}\:{positive}\:{integer}\:{n},\:\tau\left({n}\right)\:{is}\:{the}\:{number}\:{of}\:{its}\:{factors}\: \\ $$$${Prove}, \\ $$$$\sum_{{i}=\mathrm{1}} ^{{n}} \tau\left({i}\right)=\sum_{{i}=\mathrm{1}} ^{{n}} \lfloor{n}/{i}\rfloor \\ $$ Terms of Service Privacy…
Question Number 155571 by peter frank last updated on 02/Oct/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{one}\:.\mathrm{Hence} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{root}\:\mathrm{is}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{zero} \\ $$ Answered by JDamian last updated on 02/Oct/21 $${z}^{\mathrm{3}}…
Question Number 89878 by malwaan last updated on 19/Apr/20 $$\boldsymbol{{A}}\:\boldsymbol{{four\_digit}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{interesting}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}}\:\boldsymbol{{leftmost}}\:\boldsymbol{{two}} \\ $$$$\boldsymbol{{digits}}\:\boldsymbol{{is}}\:\boldsymbol{{twice}}\:\boldsymbol{{as}}\:\boldsymbol{{large}}\:\boldsymbol{{as}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{rightmost}}\:\boldsymbol{{two}}\:\boldsymbol{{digits}}. \\ $$$$\left(\boldsymbol{{for}}\:\boldsymbol{{example}}\:\mathrm{2010}\:\boldsymbol{{is}}\:\boldsymbol{{interesting}}\right) \\ $$$$\mathrm{1}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{largest}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\…