Question Number 21294 by Tinkutara last updated on 19/Sep/17 $$\mathrm{Let}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \:\mathrm{be}\:\mathrm{complex}\:\mathrm{numbers},\:\mathrm{not} \\ $$$$\mathrm{all}\:\mathrm{real},\:\mathrm{such}\:\mathrm{that}\:\mid{z}_{\mathrm{1}} \mid\:=\:\mid{z}_{\mathrm{2}} \mid\:=\:\mid{z}_{\mathrm{3}} \mid\:=\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{2}\left({z}_{\mathrm{1}} \:+\:{z}_{\mathrm{2}} \:+\:{z}_{\mathrm{3}} \right)\:−\:\mathrm{3}{z}_{\mathrm{1}} {z}_{\mathrm{2}} {z}_{\mathrm{3}}…
Question Number 21293 by Tinkutara last updated on 19/Sep/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{an}\:\mathrm{even}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{such} \\ $$$$\mathrm{that}\:\frac{{n}}{\mathrm{2}}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{let}\:\alpha_{\mathrm{0}} ,\:\alpha_{\mathrm{1}} ,\:….,\:\alpha_{{n}−\mathrm{1}} \:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{of}\:\mathrm{order}\:{n}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({a}\:+\:{b}\alpha_{{k}} ^{\mathrm{2}} \right)\:=\:\left({a}^{\frac{{n}}{\mathrm{2}}} \:+\:{b}^{\frac{{n}}{\mathrm{2}}} \right)^{\mathrm{2}}…
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Question Number 21292 by FilupS last updated on 19/Sep/17 $$\mathrm{Let}\:\:{a},{b}\in\mathbb{Z} \\ $$$$\mathrm{0}<{a}<{b} \\ $$$$\: \\ $$$$\mathrm{How}\:\mathrm{would}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}/ \\ $$$$\mathrm{largest}\:\mathrm{prime}\:\mathrm{gap}\:\mathrm{in}\:\left({a},\:{b}\right)? \\ $$$$ \\ $$$$\mathrm{Note}: \\ $$$$\mathrm{Prime}\:\mathrm{gaps}\:\mathrm{are}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \\…
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Question Number 86824 by Ar Brandon last updated on 31/Mar/20 $$\int\frac{{x}^{\mathrm{6}} +{x}^{\mathrm{2}} }{{x}^{\mathrm{8}} −{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 31/Mar/20…
Question Number 152362 by Tawa11 last updated on 27/Aug/21 $$\mathrm{f}\left(\mathrm{x}\right)\:\:\:=\:\:\:\begin{cases}{\mathrm{x}\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:,\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{0}\:\:\:<\:\:\:\mathrm{x}\:\:\:\leqslant\:\:\:\mathrm{1}}\\{\:\:\:\:\:\:\mathrm{0}\:\:\:\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\mathrm{x}\:\:\:=\:\:\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\:\mathrm{f}\:\:\:\mathrm{is}\:\mathrm{continous}\:\mathrm{but}\:\mathrm{not}\:\mathrm{of}\:\mathrm{bounded}\:\mathrm{variation} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86825 by M±th+et£s last updated on 31/Mar/20 $${a}^{\mathrm{3}} +\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=\mathrm{18} \\ $$$${a}^{\mathrm{4}} +\frac{\mathrm{1}}{{a}^{\mathrm{4}} }=? \\ $$ Commented by Ar Brandon last updated on…
Question Number 152358 by Jonathanwaweh last updated on 27/Aug/21 Commented by JDamian last updated on 27/Aug/21 $$\mathrm{5} \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 86821 by Crabby89p13 last updated on 31/Mar/20 Commented by Crabby89p13 last updated on 31/Mar/20 $${WITH}\:{LOGIC} \\ $$ Terms of Service Privacy Policy Contact:…