Question Number 84782 by mr W last updated on 16/Mar/20 $${Find}\:{the}\:{last}\:{three}\:{digits}\:{of}\:\mathrm{2019}^{\mathrm{2019}} . \\ $$ Commented by jagoll last updated on 16/Mar/20 $$\mathrm{19}^{\mathrm{2019}} \:=\:\left(\mathrm{18}+\mathrm{1}\right)^{\mathrm{2019}} \\ $$$$=\:\underset{\mathrm{i}=\mathrm{1}}…
Question Number 19245 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right) \\ $$$$\mathrm{and}\:{f}\left(\mathrm{1}\right)\:\mathrm{are}\:\mathrm{odd}\:\mathrm{integers}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{an} \\ $$$$\mathrm{integer}\:\mathrm{solution}. \\ $$ Commented by RasheedSindhi last updated…
Question Number 84783 by Power last updated on 16/Mar/20 Commented by Power last updated on 16/Mar/20 $$\mathrm{k}=\mathrm{3} \\ $$ Commented by Tony Lin last updated…
Question Number 19236 by chernoaguero@gmail.com last updated on 07/Aug/17 Answered by ,25>( last updated on 07/Aug/17 $${x}\:=\:\mathrm{2}\:\mathrm{since}\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:=\:\mathrm{13}. \\ $$ Commented by chernoaguero@gmail.com last…
Question Number 84770 by jagoll last updated on 16/Mar/20 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{30}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{x}\:\&\:\mathrm{y}\:? \\ $$ Commented by Tony Lin last updated on…
Question Number 150296 by mathdanisur last updated on 10/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150303 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\left[\mathrm{0};\infty\right)\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} +\mathrm{2}^{\boldsymbol{\mathrm{y}}} +\mathrm{2}^{\boldsymbol{\mathrm{z}}} +\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:\geqslant\:\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{xy}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{yz}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{zx}}}} +\mathrm{1} \\ $$ Answered by aleks041103 last…
Question Number 150289 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{3}} \:−\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{2}} \:=\:\mathrm{14} \\ $$$$\mathrm{Find}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{P}_{\mathrm{2}} \:=\:? \\ $$ Answered by Ar Brandon last…
Question Number 150277 by mathdanisur last updated on 10/Aug/21 $$\mathrm{Laplace}\:\mathrm{Metodu}\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{y}^{''} \:+\:\mathrm{5y}^{'} \:+\:\mathrm{6y}\:=\:\mathrm{cos}\left(\mathrm{t}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$ Commented by amin96 last updated on…
Question Number 19215 by Tinkutara last updated on 07/Aug/17 $$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:…..\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:>\:\sqrt{{n}} \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\sqrt{{n}\left({n}\:+\:\mathrm{1}\right)}\:<\:{n}\:+\:\mathrm{1} \\ $$ Answered by 433 last updated…