Question Number 151988 by mathdanisur last updated on 24/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\:\:\mathrm{are}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\mathrm{2x}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{y}^{\boldsymbol{\mathrm{y}}} \:=\:\mathrm{3z}^{\boldsymbol{\mathrm{z}}} \\ $$$$\mathrm{then}\:\mathrm{find}\:\:\frac{\mathrm{2021}\boldsymbol{\mathrm{x}}\:+\:\mathrm{2022}\boldsymbol{\mathrm{y}}\:+\:\mathrm{2023}\boldsymbol{\mathrm{z}}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}}\:=\:? \\ $$ Commented by mathdanisur last updated on 25/Aug/21…
Question Number 20914 by Tinkutara last updated on 07/Sep/17 $$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{equation}\:{p}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{with} \\ $$$$\mathrm{real}\:\mathrm{coefficients}\:\mathrm{has}\:\mathrm{purely}\:\mathrm{imaginary} \\ $$$$\mathrm{roots}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{equation}\:{p}\left({p}\left({x}\right)\right)\:=\:\mathrm{0} \\ $$$$\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Only}\:\mathrm{purely}\:\mathrm{imaginary}\:\mathrm{roots} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{All}\:\mathrm{real}\:\mathrm{roots} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Two}\:\mathrm{real}\:\mathrm{and}\:\mathrm{two}\:\mathrm{purely}\:\mathrm{imaginary} \\ $$$$\mathrm{roots} \\…
Question Number 151979 by mathdanisur last updated on 24/Aug/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{mx}\right)^{\boldsymbol{\mathrm{n}}} \:-\:\left(\mathrm{1}+\mathrm{nx}\right)^{\boldsymbol{\mathrm{m}}} }{\mathrm{x}^{\mathrm{2}} }\:=\:?\:\:;\:\:\mathrm{m};\mathrm{n}\in\mathbb{N} \\ $$ Answered by mr W last updated on 24/Aug/21 $$\left(\mathrm{1}+{mx}\right)^{{n}}…
Question Number 151956 by mathdanisur last updated on 24/Aug/21 $$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:\mathrm{arctan}\:\frac{\mathrm{2k}^{\mathrm{2}} \:-\:\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86426 by M±th+et£s last updated on 28/Mar/20 $${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$ Answered by mr W last updated on 28/Mar/20 $${let}\:{x}={n}+\delta \\…
Question Number 20882 by soufiane zarik last updated on 06/Sep/17 Answered by $@ty@m last updated on 08/Sep/17 Commented by soufiane zarik last updated on 11/Sep/17…
Question Number 20881 by tawa tawa last updated on 05/Sep/17 Answered by mrW1 last updated on 06/Sep/17 $$\left(\mathrm{ax}+\mathrm{ay}\right)^{\mathrm{n}} =\mathrm{a}^{\mathrm{n}} \left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{n}} \\ $$$$\mathrm{since}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{exists},\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}. \\ $$$$\mathrm{its}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{is} \\…
Question Number 151948 by mathdanisur last updated on 24/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86396 by opk2k6@gmail.com last updated on 28/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20867 by Tinkutara last updated on 05/Sep/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{irrational}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{21}\:\mathrm{is} \\ $$ Answered by alex041103 last updated on 09/Sep/17 $$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left(\mathrm{3}{x}−\mathrm{2}\right)\left(\mathrm{3}{x}+\mathrm{1}\right)= \\…