Question Number 188226 by Shrinava last updated on 26/Feb/23 $$\mathrm{If}\:\:\:\Omega\:=\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{sin}\left(\mathrm{A}\:−\:\frac{\pi}{\mathrm{6}}\right)}{\mathrm{cos}\left(\mathrm{B}\:−\:\frac{\pi}{\mathrm{6}}\right)\mathrm{cos}\left(\mathrm{C}\:−\:\frac{\pi}{\mathrm{6}}\right)}\:\:\:\mathrm{in}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{4}\Omega\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{6}\Omega\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\Omega\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by aleks041103 last updated…
Question Number 57127 by ANTARES VY last updated on 30/Mar/19 $$\left\{\boldsymbol{\mathrm{cos}}\mathrm{1}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{2}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{3}°\right\}+….+\left\{\boldsymbol{\mathrm{cos}}\mathrm{270}\right\}=? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19 $$\boldsymbol{{source}}\:\boldsymbol{{S}}.\boldsymbol{{L}}\:\boldsymbol{{Loney}}\:\boldsymbol{{great}}\:\boldsymbol{{mathematician}} \\ $$ Commented by…
Question Number 122658 by mathocean1 last updated on 18/Nov/20 $${we}\:{are}\:{in}\:\mathbb{C}^{\mathrm{3}} . \\ $$$$\left({S}\right):\:\:\begin{cases}{{x}+{y}+{z}=\mathrm{2}{i}−\mathrm{1}\:{and}\:{xyz}=\mathrm{2}}\\{{xy}+{yz}+{xz}=−\mathrm{2}\left(\mathrm{1}+{i}\right)\:}\end{cases} \\ $$$${P}\left({z}\right)={z}^{\mathrm{3}} +\left(\mathrm{1}−\mathrm{2}{i}\right){z}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{1}+{i}\right)−\mathrm{2}. \\ $$$${show}\:{that}\:\left({a},{b},{c}\right)\:{is}\:{solution} \\ $$$${of}\:\left({S}\right)\:{if}\:{and}\:{only}\:{a};{b};{c}\:{are}\: \\ $$$${roots}\:{of}\:{P}. \\ $$…
Question Number 122653 by mathocean1 last updated on 18/Nov/20 $${we}\:{define}\:{in}\:{base}\:{x}\:{the}\: \\ $$$${number}\:{y}\:{and}\:{z}\:{by}: \\ $$$${y}=\overline {\mathrm{123}}\:^{{x}\:} {and}\:{z}=\overline {\mathrm{201}}\:^{{x}} \\ $$$$\left.\mathrm{1}\right)\:{without}\:{knowing}\:{x},\:{write} \\ $$$${the}\:{product}\:{x}×{y}×{z}\:{in}\:{function} \\ $$$${of}\:{x}. \\ $$$$\left.\mathrm{2}\right)\:{we}\:{suppose}\:{that}\:{x}+{y}+{z}=\mathrm{92}…
Question Number 122651 by mathocean1 last updated on 18/Nov/20 $${show}\:{that}\:{if}\: \\ $$$$\mathrm{5}^{\mathrm{3}{n}} +\mathrm{5}^{\mathrm{2}{n}} +\mathrm{5}^{{n}} +\mathrm{1}\:{is}\:{divisible}\:{by} \\ $$$$\mathrm{13},\:{then}\:{n}\:\left(\in\:\mathbb{N}\right)\:{is}\:{not}\:{a}\: \\ $$$${multiple}\:{of}\:\mathrm{4}. \\ $$ Answered by mindispower last…
Question Number 122649 by mathocean1 last updated on 18/Nov/20 $${By}\:{divising}\:{an}\:{integer}\:{a}\:{by}\: \\ $$$${integer}\:{b}\:{we}\:{find}\:{the}\:{result}: \\ $$$$\mathrm{0}.\mathrm{285714285714}…\:{followed} \\ $$$${by}\:{a}\:{group}\:{of}\:\mathrm{6}\:{digits}:\:\mathrm{285714} \\ $$$${which}\:{is}\:{repeated}\:{indefinited}. \\ $$$${determinate}\:{the}\:{fraction}\:\frac{{a}}{{b}}\: \\ $$$$ \\ $$$$ \\…
Question Number 122648 by mathocean1 last updated on 18/Nov/20 $${Determinate}\:{the}\:{values}\:{of}\:{n}\:\in\:\mathbb{N} \\ $$$${such}\:{that}\:{n}−\mathrm{1}\:{can}\:{divise}\:\mathrm{2}{n}+\mathrm{3} \\ $$ Answered by TANMAY PANACEA last updated on 18/Nov/20 $$\mathrm{2}{n}−\mathrm{2}+\mathrm{5}\:\:\:{when}\:{devided}\:{by}\:{n}−\mathrm{1} \\ $$$$\mathrm{2}+\frac{\mathrm{5}}{{n}−\mathrm{1}}\:\:\:\:\:{n}\:{should}\:{be}\:\mathrm{6}…
Question Number 122646 by mathocean1 last updated on 18/Nov/20 $${Determinate}\:{the}\:{couples}\: \\ $$$$\left({a};\:{b}\right)\:{such}\:{that}\: \\ $$$${GCD}\left({a};{b}\right)+{LCM}\left({a};{b}\right)={a}+{b} \\ $$$${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$$${LCM}:\:{least}\:{common}\:{multiple} \\ $$ Commented by mathocean1 last updated…
Question Number 122647 by mathocean1 last updated on 18/Nov/20 $${p}\:\in\:\mathbb{Z}.\:{given}: \\ $$$${u}=\mathrm{14}{p}+\mathrm{3}\:;\:{v}=\mathrm{5}{p}+\mathrm{1}, \\ $$$$\left({E}\right):\mathrm{87}{x}+\mathrm{31}{y}=\mathrm{2}\:;\:{we}\:{have}\: \\ $$$${also}\:{the}\:{line}\:\left({D}\right):\:\mathrm{87}{x}−\mathrm{31}{y}=\mathrm{2} \\ $$$$\left.\mathrm{1}\right){show}\:{that}\:{u}\:{and}\:{v}\:{are}\:{primes} \\ $$$${between}\:{them}.\left({i}\:{mean}\:{the}\:\right. \\ $$$${don}'{t}\:{have}\:{any}\:{common}\:{divisor}\: \\ $$$$\left.{excepted}\:\mathrm{1}\:{and}\:−\mathrm{1}.\right) \\…
Question Number 122640 by Eric002 last updated on 18/Nov/20 $${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{1} \\ $$$${find}\:{f}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com