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Category: Algebra

Find-cos-3pi-7-cos-3pi-7-2-2cos-3pi-7-

Question Number 154892 by mathdanisur last updated on 22/Sep/21 $$\mathrm{Find}: \\ $$$$\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:+\:\mathrm{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:\sqrt{\mathrm{2}\:-\:\mathrm{2cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}\:=\:? \\ $$ Commented by MJS_new last updated on 23/Sep/21 $$\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented…

2x-1-2-8-2xy-4-4y-8xy-1-1-

Question Number 89344 by jagoll last updated on 17/Apr/20 $$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{8}\sqrt{\mathrm{2}{xy}}\:=\:\mathrm{4} \\ $$$$\mathrm{4}{y}−\sqrt{\mathrm{8}{xy}−\mathrm{1}}\:=\:\mathrm{1} \\ $$ Commented by john santu last updated on 17/Apr/20 $$\mathrm{8}{xy}−\mathrm{1}\:=\:\mathrm{16}{y}^{\mathrm{2}} −\mathrm{8}{y}+\mathrm{1}…

Question-89292

Question Number 89292 by student work last updated on 16/Apr/20 Answered by jagoll last updated on 16/Apr/20 $${x}+{y}\:=\:\mathrm{20}\:\left({i}\right) \\ $$$${y}+{z}\:=\:\mathrm{10}\:\left({ii}\right) \\ $$$${x}+{u}\:=\:\mathrm{24}\:\left({iii}\right) \\ $$$$\frac{{u}}{{z}}\:=\:\mathrm{7}\:\Rightarrow{u}\:=\:\mathrm{7}{z}\:\left({iv}\right) \\…

Question-154805

Question Number 154805 by mathdanisur last updated on 21/Sep/21 Commented by TheHoneyCat last updated on 21/Sep/21 Hi @Mathdanisur, I don't want to get personal or anything, but how do you manage to find so many questions per day? It's just incredible... Are you an exercise creator or something? Anyway, thanks for what you do, I've already found the solutions to 10 to 20 of your problems, and I look forward to attempt (and mostly fail) to solve many more. With respect, TheHoneyCat Commented by mathdanisur last updated on 21/Sep/21 Dear Ser thank you, your problems are amazing and interesting, I have and liking towards it…

Solve-for-real-numbers-5-5-x-1-5-5-5-x-1-5-2-1-5-

Question Number 154804 by mathdanisur last updated on 21/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt[{\mathrm{5}}]{\mathrm{5}\sqrt{\mathrm{5}}\:+\:\mathrm{x}}\:-\:\sqrt[{\mathrm{5}}]{\mathrm{5}\sqrt{\mathrm{5}}\:-\:\mathrm{x}}\:=\:\sqrt[{\mathrm{5}}]{\mathrm{2}} \\ $$ Commented by 7770 last updated on 21/Sep/21 $$\mathrm{x}=\mathrm{11} \\ $$ Answered…

Please-help-with-this-summation-k-0-n-1-k-n-C-k-y-n-k-

Question Number 89268 by I want to learn more last updated on 16/Apr/20 $$\boldsymbol{\mathrm{Please}}\:\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{summation}}. \\ $$$$\:\:\:\underset{\boldsymbol{\mathrm{k}}\:\:=\:\:\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\left(−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{k}}} \:\:\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\boldsymbol{\mathrm{k}}} \:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}\:\:−\:\:\boldsymbol{\mathrm{k}}} \:\:\:\:=\:\:\:??? \\ $$ Terms…