Question Number 124690 by mathocean1 last updated on 05/Dec/20 $${show}\:{that}\:\forall\:{a},{b}\in\mathbb{N}^{\ast} \:{if}\:\delta={GCD}\left({a};{b}\right)\: \\ $$$${then}\:\delta\mathbb{Z}=\left\{{au}+{bv};\:{u}\:{and}\:{v}\:\in\mathbb{Z}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124688 by mathocean1 last updated on 05/Dec/20 $${Solve}\:{in}\:\mathbb{N}^{\mathrm{2}} : \\ $$$${a}.\:\:\begin{cases}{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} =\mathrm{4704}}\\{{GCD}\left({a};{b}\right)=\mathrm{7}}\end{cases} \\ $$$${b}.\:\:\:\begin{cases}{\mathrm{13}{GCD}\left({a};{b}\right)−\mathrm{2}{SCM}\left({a};{b}\right)=\mathrm{4}}\\{\mathrm{3}<{GCD}\left({a};{b}\right)<\mathrm{7}}\end{cases} \\ $$$$ \\ $$$${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$$${SCM}:\:{smallest}\:{common}\:{multiple} \\ $$…
Question Number 124691 by mathocean1 last updated on 05/Dec/20 $${show}\:{that}\:{the}\:{set}\:{of}\:{prime}\:{numbers} \\ $$$${is}\:{infinite} \\ $$ Answered by MJS_new last updated on 05/Dec/20 $$\mathrm{suppose}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{primes}\:\mathrm{is}\:\mathrm{finite}\:\mathrm{and}\:\mathrm{is}\:{n} \\ $$$$\mathrm{let}\:{N}=\mathrm{1}+\underset{{j}=\mathrm{1}} {\overset{{n}}…
Question Number 124681 by mathocean1 last updated on 05/Dec/20 $${solve}\:{in}\:\mathbb{Z}^{\mathrm{2}} \:\: \\ $$$$\left({E}\right):\:\mathrm{3}{x}−{y}=\mathrm{4} \\ $$ Answered by Ar Brandon last updated on 05/Dec/20 $$\left(\mathrm{x},\mathrm{y}\right)=\left(\mathrm{2},\mathrm{2}\right) \\…
Question Number 59131 by naka3546 last updated on 05/May/19 $${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R} \\ $$$${a}\:+\:{b}\:+\:{c}\:\:=\:\:\mathrm{5} \\ $$$${Prove}\:\:{that} \\ $$$$\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:−\:\mathrm{2}{b}\:+\:\mathrm{1}}\:\:+\:\:\sqrt{{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:\mathrm{2}{c}\:+\:\mathrm{1}}\:\:+\:\:\sqrt{{c}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} \:−\:\mathrm{2}{a}\:+\:\mathrm{1}}\:\:\:\geqslant\:\:\sqrt{\mathrm{29}} \\ $$ Answered…
Question Number 190199 by 073 last updated on 29/Mar/23 Answered by mr W last updated on 29/Mar/23 $${min}=\mathrm{0}\:{when}\:{z}=\mathrm{4}−\mathrm{3}{i} \\ $$ Commented by 073 last updated…
Question Number 124663 by mohammad17 last updated on 05/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 190198 by 073 last updated on 29/Mar/23 Answered by Rasheed.Sindhi last updated on 29/Mar/23 $$\mathrm{A}\in\mathbb{R}\Rightarrow \\ $$$$\mathrm{2}{x}−\mathrm{3}\geqslant\mathrm{0}\:\wedge\:\mathrm{3}−\mathrm{2}{x}\geqslant\mathrm{0} \\ $$$$\:\:{x}\geqslant\frac{\mathrm{3}}{\mathrm{2}}\:\wedge\:{x}\leqslant\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow{x}=\frac{\mathrm{3}}{\mathrm{2}}\notin\mathbb{Z} \\ $$$$\mathrm{A}=\frac{\mathrm{4}\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{3}+\mathrm{0}+\mathrm{0}}{\mathrm{2}\left(\frac{\mathrm{3}}{\mathrm{2}}\right)}=\frac{\mathrm{9}+\mathrm{3}}{\mathrm{3}}=\mathrm{4} \\…
Question Number 59121 by naka3546 last updated on 05/May/19 Answered by mr W last updated on 05/May/19 $${cirvle}\:\mathrm{1}:\: \\ $$$${r}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{\mathrm{1}} ={square}\:{side}\:{length} \\…
Question Number 59113 by naka3546 last updated on 04/May/19 $${Let}\:\:{a}\:\:{is}\:\:{a}\:\:{real}\:\:{number}\:.\:\:{How}\:\:{many}\:\:{solutions} \\ $$$${can}\:\:{the}\:\:{equation}\:\:{in}\:\:\theta\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\right)\left(\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\:\:=\:\:{a} \\ $$$${have}\:\:{for}\:\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{2}}\:\:? \\ $$ Answered by MJS last updated on 05/May/19…