Question Number 49237 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $${Find}\:{a}\:{polynomial}\:{f}\left({x}\right)\in{Q}\left[{x}\right]\:{such} \\ $$$${that}\:{its}\:{main}\:{coefficient}\:{is}\:\mathrm{1}\:{and}\: \\ $$$$\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\in{V}\left({f}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 49238 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $${Find}\:{the}\:{maximum}\:{common}\:{divisor} \\ $$$${of}\:{the}\:{folllwing}\:{polynomials}: \\ $$$$\bullet{f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\: \\ $$$${g}\left({x}\right)=−\mathrm{3}{x}^{\mathrm{4}} −{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} \:{in}\:{Q}\left[{x}\right]. \\ $$$$\bullet{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}\:{and}\:{g}\left({x}\right)={x}^{\mathrm{4}}…
Question Number 49235 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $${Let}\:{A}\:{a}\:{conmutative}\:{ring}\:{with}\:\mathrm{1}\: \\ $$$$\left({not}\:{necessarily}\:{a}\:{whole}\:{domain}\right). \\ $$$${Study}\:{the}\:{structure}\:{that}\:{has}\:{A}\left({x}\right)\: \\ $$$${with}\:{the}\:{usual}\:{operations} \\ $$$${Is}\:{it}\:{a}\:{ring}\:{always}? \\ $$$${Is}\:{it}\:{a}\:{whole}\:{domain}? \\ $$$${How}\:{are}\:{the}\:{units}? \\ $$ Terms…
Question Number 49229 by munnabhai455111@gmail.com last updated on 04/Dec/18 $$\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{{y}}^{\mathrm{2}} \\ $$ Commented by Abdo msup. last updated on 04/Dec/18 $${factorisation} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}}…
Question Number 114758 by bobhans last updated on 21/Sep/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\mathrm{4}{n}^{\mathrm{2}} \left(\mathrm{10}{n}−\mathrm{6}\right)\left(\mathrm{10}{n}−\mathrm{4}\right)}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{10}{n}−\mathrm{1}\right)\left(\mathrm{10}{n}+\mathrm{1}\right)}\:=? \\ $$ Answered by Olaf last updated on 21/Sep/20 $${u}_{{n}} \:=\:\frac{\mathrm{4}{n}^{\mathrm{2}}…
Question Number 49220 by malwaan last updated on 04/Dec/18 $$\left(\mathrm{1}+\mathrm{x}−\mathrm{2x}^{\mathrm{2}} \:\right)^{\mathrm{8}} =? \\ $$ Commented by Abdo msup. last updated on 04/Dec/18 $${S}\:=\sum_{{k}=\mathrm{0}} ^{\mathrm{8}} \:{C}_{\mathrm{8}}…
Question Number 114739 by mr W last updated on 20/Sep/20 $${find}\:{the}\:{largest}\:{and}\:{smallest} \\ $$$${coefficient}\:{in}\:\left(\mathrm{4}+\mathrm{3}{x}\right)^{−\mathrm{5}} . \\ $$ Answered by mr W last updated on 20/Sep/20 $$\left(\mathrm{4}+\mathrm{3}{x}\right)^{−\mathrm{5}}…
Question Number 180272 by Shrinava last updated on 09/Nov/22 $$\mathrm{In}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{following}\:\mathrm{identity} \\ $$$$\mathrm{is}\:\mathrm{true}:\:\:\:\mathrm{6R}^{\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:\:,\:\:\:\mathrm{a}\:\neq\:\mathrm{c}. \\ $$$$\mathrm{Ptove}\:\mathrm{that}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{line}\:\mathrm{is}\:\mathrm{antiparallel}\:\mathrm{to}\:\:\mathrm{AC}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 180273 by Shrinava last updated on 09/Nov/22 $$\mathrm{In}\:\mathrm{triangle}\:\:\mathrm{ABC}\:\:\mathrm{with}\:\mathrm{angles}\:\:\alpha\:,\:\beta\:,\:\gamma \\ $$$$\mathrm{correspondently}\:,\:\mathrm{Euler}'\mathrm{s}\:\mathrm{line}\:\mathrm{interescts} \\ $$$$\mathrm{BC}\:\:\mathrm{at}\:\mathrm{point}\:\:\mathrm{P}.\:\mathrm{Ite}'\mathrm{s}\:\mathrm{put}\:\:\delta\:\:\mathrm{is}\:\mathrm{angle} \\ $$$$\mathrm{between}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{line}\:\mathrm{and}\:\:\mathrm{BC}\:\left(\angle\mathrm{BPH}\right). \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true} \\ $$$$\mathrm{tan}\:\delta\:=\:\frac{\mathrm{2}\:\mathrm{cos}\:\beta\:\mathrm{cos}\:\gamma\:−\:\mathrm{cos}\:\alpha}{\mathrm{sin}\:\left(\beta\:−\:\gamma\right)} \\ $$ Terms of Service…
Question Number 180274 by Ar Brandon last updated on 09/Nov/22 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{C}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{z}^{\mathrm{4}} +\left(\mathrm{7}−{i}\right){z}^{\mathrm{3}} +\left(\mathrm{12}−\mathrm{15}{i}\right){z}^{\mathrm{2}} +\left(\mathrm{4}+\mathrm{4}{i}\right){z}+\mathrm{16}+\mathrm{192}{i}=\mathrm{0} \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{it}\:\mathrm{has}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{and}\:\mathrm{a}\:\mathrm{purely}\:\mathrm{imaginary}\:\mathrm{root} \\ $$$$\mathrm{of}\:\mathrm{equal}\:\mathrm{magnitude}. \\ $$ Answered by Frix…