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Category: Algebra

Question-154429

Question Number 154429 by liberty last updated on 18/Sep/21 Commented by liberty last updated on 18/Sep/21 $$ \\ $$$$\:{A}=\sqrt[{\mathrm{3}}]{−\mathrm{15}+\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}}+\sqrt[{\mathrm{3}}]{−\mathrm{15}−\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}} \\ $$$$ \\ $$ Commented by…

Prove-that-1-m-C-0-n-m-1-C-1-n-n-1-m-2-C-2-n-n-1-2-1-m-n-C-n-m-n-1-m-n-2-m-2n-m-n-

Question Number 23357 by Tinkutara last updated on 29/Oct/17 $${Prove}\:{that}\:\frac{\mathrm{1}}{{m}!}{C}_{\mathrm{0}} +\frac{{n}}{\left({m}+\mathrm{1}\right)!}{C}_{\mathrm{1}} +\frac{{n}\left({n}−\mathrm{1}\right)}{\left({m}+\mathrm{2}\right)!}{C}_{\mathrm{2}} \\ $$$$+…+\frac{{n}\left({n}−\mathrm{1}\right)…\mathrm{2}.\mathrm{1}}{\left({m}+{n}\right)!}{C}_{{n}} = \\ $$$$\frac{\left({m}+{n}+\mathrm{1}\right)\left({m}+{n}+\mathrm{2}\right)…\left({m}+\mathrm{2}{n}\right)}{\left({m}+{n}\right)!}. \\ $$ Terms of Service Privacy Policy Contact:…

Question-88881

Question Number 88881 by Power last updated on 13/Apr/20 Answered by mahdi last updated on 13/Apr/20 $$\mathrm{A}=\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−…}}}}}} \\ $$$$\mathrm{A}=\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\mathrm{A}}}}\Rightarrow\mathrm{A}^{\mathrm{2}} =\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\mathrm{A}}} \\ $$$$\mathrm{A}\backsimeq\mathrm{2}.\mathrm{5070} \\ $$ Terms…

3-x-2-5-gt-x-1-

Question Number 88873 by jagoll last updated on 13/Apr/20 $$\mathrm{3}+\sqrt{{x}^{\mathrm{2}} −\mathrm{5}}\:>\:\mid{x}−\mathrm{1}\mid\: \\ $$ Commented by john santu last updated on 13/Apr/20 $$\Rightarrow\left(\mathrm{3}+\sqrt{{x}^{\mathrm{2}} −\mathrm{5}}\right)^{\mathrm{2}} \:>\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\…

x-y-y-x-82-x-x-y-y-83-9-5-x-y-

Question Number 154400 by mathdanisur last updated on 18/Sep/21 $$\mathrm{x}\sqrt{\mathrm{y}}\:-\:\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{82} \\ $$$$\mathrm{x}\sqrt{\mathrm{x}}\:+\:\mathrm{y}\sqrt{\mathrm{y}}\:=\:\mathrm{83} \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\:\centerdot\:\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:? \\ $$ Answered by TheHoneyCat last updated on 20/Sep/21 $$\mathrm{just}\:\mathrm{so}\:\mathrm{you}\:\mathrm{understand}\:\mathrm{my}\:\mathrm{mess}\:\left(\mathrm{1}\right)\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{first}\:\mathrm{equation}\:\mathrm{and}\:\left(\mathrm{2}\right)\:\mathrm{the}\:\mathrm{other} \\…

prove-that-the-sum-2-2-2-2-3-2-4-2-2019-2-2020-is-divisible-by-30-

Question Number 154401 by mathdanisur last updated on 18/Sep/21 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{2}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +…+\mathrm{2}^{\mathrm{2019}} +\mathrm{2}^{\mathrm{2020}} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\:\mathrm{by}\:\:\mathrm{30} \\ $$ Answered by talminator2856791 last updated…