Question Number 140774 by ajfour last updated on 12/May/21 $${Prove}\:{that} \\ $$$$\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} =\:\sqrt{\mathrm{2}} \\ $$ Commented by ajfour last updated on 12/May/21 $${All}\:{are}\:{Excellent}\:{solutions}\:: \\…
Question Number 9517 by Joel575 last updated on 12/Dec/16 $${f}\left(\mathrm{1}\right)\:+\:{f}\left(\mathrm{2}\right)\:+\:{f}\left(\mathrm{3}\right)\:+\:…\:+\:{f}\left({n}\right)\:=\:{n}^{\mathrm{2}} .\:{f}\left({n}\right) \\ $$$${n}\:>\:\mathrm{1};\:{f}\left(\mathrm{1}\right)\:=\:\mathrm{2016} \\ $$$$\mathrm{So},\:{f}\left(\mathrm{2016}\right)\:=\:? \\ $$ Commented by sou1618 last updated on 12/Dec/16 $$…
Question Number 9484 by Joel575 last updated on 10/Dec/16 $$\mathrm{S}\left({r}\right)\:=\:\mathrm{12}\:+\:\mathrm{12}{r}^{\mathrm{1}} \:+\:\mathrm{12}{r}^{\mathrm{2}} \:+\:\mathrm{12}{r}^{\mathrm{3}} \:+\:\mathrm{12}{r}^{\mathrm{4}} \:+\:… \\ $$$$\mathrm{with}\:−\mathrm{1}\:<\:{r}\:<\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{If}\:\:\mathrm{S}\left({a}\right)\:.\:\mathrm{S}\left(−{a}\right)\:=\:\mathrm{2016},\:\mathrm{with}\:−\mathrm{1}\:<\:{a}\:<\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{S}\left({a}\right)\:+\:\mathrm{S}\left(−{a}\right)\:? \\ $$ Answered…
Question Number 9460 by tawakalitu last updated on 09/Dec/16 Answered by sou1618 last updated on 09/Dec/16 $$\sqrt{\mathrm{11}−\mathrm{2}}=\sqrt{\mathrm{10}+\mathrm{1}−\mathrm{2}}=\sqrt{\mathrm{9}}=\mathrm{3} \\ $$$$\sqrt{\mathrm{1111}−\mathrm{22}}=\sqrt{\mathrm{1000}+\mathrm{100}+\mathrm{10}+\mathrm{1}−\mathrm{20}−\mathrm{2}}=\sqrt{\mathrm{1089}}=\mathrm{33} \\ $$$$…… \\ $$$${X}=\sqrt{\mathrm{1111}……\mathrm{11}_{\mathrm{2000}{digits}} −\mathrm{22}…\mathrm{2}_{\mathrm{1000}{digits}} }…
Question Number 74970 by mr W last updated on 05/Dec/19 $${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{3} \\ $$$$ \\ $$$${find}…
Question Number 74948 by vishalbhardwaj last updated on 04/Dec/19 $$\mathrm{The}\:\mathrm{hhpotenuse}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle} \\ $$$$\mathrm{has}\:\mathrm{its}\:\mathrm{ends}\:\mathrm{at}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{and}\:\left(−\mathrm{4},\mathrm{1}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{legs}\:\left(\mathrm{perpendicar}\right. \\ $$$$\left.\:\mathrm{sides}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}. \\ $$ Answered by MJS last updated on 04/Dec/19…
Question Number 9391 by Joel575 last updated on 04/Dec/16 $$\underset{{n}=\mathrm{2}} {\overset{\mathrm{100}} {\sum}}\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{{n}^{\mathrm{2}\:} }\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74923 by aliesam last updated on 04/Dec/19 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{3}} =\left[\frac{{n}\left({n}+\mathrm{1}\right)\:}{\mathrm{2}}\right]^{\mathrm{2}} \\ $$ Commented by aliesam last updated on 04/Dec/19 $${god}\:{bless}\:{you} \\ $$…
Question Number 9379 by FilupSmith last updated on 03/Dec/16 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−{n}\right)^{\mathrm{1}−{n}} \\ $$$${S}=?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9325 by tawakalitu last updated on 30/Nov/16 Answered by RasheedSoomro last updated on 30/Nov/16 $$\left(\mathrm{B}\right)\:\mathrm{12}\: \\ $$$$\mathrm{25}\equiv−\mathrm{1}\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$$$\left(\mathrm{25}\right)^{\mathrm{15}} \equiv\left(−\mathrm{1}\right)^{\mathrm{15}} \left(\mathrm{mod}\:\mathrm{13}\right) \\ $$$$\left(\mathrm{25}\right)^{\mathrm{15}}…