Question Number 7294 by Tawakalitu. last updated on 21/Aug/16 $${If}\:{a}\:{polynomial}\:{p}\left({x}\right)\:{satisfies}\:{the}\:{identity} \\ $$$$ \\ $$$${x}^{\mathrm{2015}} \:+\:{x}^{\mathrm{2014}} \:+\:{x}^{\mathrm{2013}} \:+\:\mathrm{1}\:=\:\left({x}^{\mathrm{3}} \:+\:{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{1}\right){p}\left({x}\right) \\ $$$$ \\ $$$${Find}\:\:{p}\left(−\mathrm{1}\right) \\ $$…
Question Number 138367 by KwesiDerek last updated on 12/Apr/21 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{−\mathrm{2}} =\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{16}} +\boldsymbol{\mathrm{x}}^{−\mathrm{16}} =? \\ $$ Commented by Kamel last updated on 12/Apr/21…
Question Number 138366 by KwesiDerek last updated on 12/Apr/21 $$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{−\mathrm{2}} =\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{16}} +\boldsymbol{\mathrm{x}}^{−\mathrm{16}} =? \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{help}} \\ $$ Answered by TheSupreme last updated…
Question Number 72824 by Rio Michael last updated on 03/Nov/19 $${fnd}\:{all}\:{integers}\:{n}\:{for}\:{which}\: \\ $$$$\:\mathrm{13}\mid\:\mathrm{4}\left({n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$ Answered by mind is power last updated on 03/Nov/19…
Question Number 7289 by FilupSmith last updated on 21/Aug/16 $$\mathrm{For}\:\mathrm{any}\:\mathrm{number}\:{x}>\mathrm{1}:{x}\in\mathbb{Z} \\ $$$${x}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{a}\:\mathrm{combination} \\ $$$$\mathrm{of}\:\mathrm{numbers}\:\mathrm{multiplied}\:\mathrm{together}. \\ $$$$\mathrm{e}.\mathrm{g}. \\ $$$$\mathrm{10}=\mathrm{5}×\mathrm{2} \\ $$$$\mathrm{20}=\mathrm{5}×\mathrm{4}=\mathrm{5}×\mathrm{2}×\mathrm{2} \\ $$$$\mathrm{100}=\mathrm{10}×\mathrm{10}=\mathrm{5}×\mathrm{2}×\mathrm{5}×\mathrm{2} \\ $$$$\: \\…
Question Number 138362 by mohammad17 last updated on 12/Apr/21 $${prove}\:{that}\: \\ $$$$ \\ $$$$\left(\mathrm{1}+{i}\right)^{{n}} +\left(\mathrm{1}−{i}\right)^{{n}} =\mathrm{2}^{\frac{{n}+\mathrm{1}}{\mathrm{2}}} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 7287 by sarathon last updated on 21/Aug/16 $$\mathrm{7}{a}_{\mathrm{1}} +\mathrm{7}^{\mathrm{2}} {a}_{\mathrm{2}} +\centerdot\centerdot\centerdot+\mathrm{7}^{{n}} {a}_{{n}} =\mathrm{3}^{{n}} −\mathrm{1} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{a}_{{n}} }{\mathrm{3}^{{n}−\mathrm{1}} }=? \\ $$ Commented…
Question Number 72823 by Raxreedoroid last updated on 03/Nov/19 $$\mathrm{What}\:\mathrm{is}\:\mathrm{derivative}\:\mathrm{for}\:\mathrm{this}\:\mathrm{function} \\ $$$$\: \\ $$$${a}×{b}^{{x}−\mathrm{1}} ×{c}^{\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)} ×{d}^{\frac{\mathrm{1}}{\mathrm{6}}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)} \\ $$ Answered by mind is power last updated…
Question Number 138355 by mohammad17 last updated on 12/Apr/21 Commented by mohammad17 last updated on 12/Apr/21 $${help}\:{me}\:{sir} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 138348 by EnterUsername last updated on 12/Apr/21 Commented by EnterUsername last updated on 12/Apr/21 Image courtesy of Anna Lachowska. Terms of Service Privacy…