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Category: Algebra

show-that-2-3-5-33-18-1-3-2-3-5-33-18-1-3-1-

Question Number 89086 by M±th+et£s last updated on 15/Apr/20 $${show}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{5}\sqrt{\mathrm{33}}}{\mathrm{18}}}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{5}\sqrt{\mathrm{33}}}{\mathrm{18}}}=\mathrm{1} \\ $$ Commented by MJS last updated on 15/Apr/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong}. \\ $$ Terms…

There-are-3-or-more-profiles-of-this-person-and-I-mentioned-it-he-knowes-who-he-and-that-person-paints-what-I-share-in-red-do-his-best-nothing-will-chang-

Question Number 154613 by mathdanisur last updated on 20/Sep/21 $$\mathrm{There}\:\mathrm{are}\:\mathrm{3}\:\mathrm{or}\:\mathrm{more}\:\mathrm{profiles}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{person}\:\mathrm{and}\:\mathrm{I}\:\mathrm{mentioned}\:\mathrm{it},\:\mathrm{he}\:\mathrm{knowes} \\ $$$$\mathrm{who}\:\mathrm{he}\:\mathrm{and}\:\mathrm{that}\:\mathrm{person}\:\mathrm{paints}\:\mathrm{what} \\ $$$$\mathrm{I}\:\mathrm{share}\:\mathrm{in}\:\mathrm{red},\:\mathrm{do}\:\mathrm{his}\:\mathrm{best},\:\mathrm{nothing}\:\mathrm{will} \\ $$$$\mathrm{chang}! \\ $$ Commented by liberty last updated…

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Question Number 89070 by ajfour last updated on 15/Apr/20 $$\frac{\sqrt{{a}^{\mathrm{2}} +\frac{{b}^{\mathrm{2}} }{{x}^{\mathrm{2}} }}+\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} {x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} +\frac{{b}^{\mathrm{2}} }{{x}^{\mathrm{2}} }}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} {x}^{\mathrm{2}} }}\:=\:\left(\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\right){x} \\…

let-x-y-z-gt-0-prove-that-z-x-2-y-2-2-2-z-x-y-2xy-x-y-

Question Number 154596 by mathdanisur last updated on 19/Sep/21 $$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{z}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }}\:+\:\sqrt{\mathrm{2}}\:\geqslant\:\mathrm{2}\:\sqrt{\frac{\mathrm{z}}{\mathrm{x}+\mathrm{y}}}\:+\:\frac{\sqrt{\mathrm{2xy}}}{\mathrm{x}+\mathrm{y}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-1-2-1-3-1-1-2-1-3-1-4-1-1-3-1-4-1-5-

Question Number 89064 by john santu last updated on 15/Apr/20 $$\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{…}}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{…}}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\mathrm{5}\sqrt{…}}}}}}\:=\:… \\ $$ Answered by M±th+et£s last updated on 16/Apr/20 $$\mathrm{3}=\sqrt{\mathrm{1}+\mathrm{8}}=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{16}}}=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{25}}}} \\ $$$$=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{36}}}}}=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\mathrm{5}\sqrt{\mathrm{49}}}}}……} \\ $$$$=…………=\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\mathrm{5}\sqrt{\mathrm{1}+\mathrm{6}\sqrt{\mathrm{1}+…..}}}}}}…