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Category: Algebra

If-x-gt-0-and-the-4-th-term-in-the-expansion-of-2-3-8-x-10-has-maximum-value-then-find-the-range-of-x-

Question Number 22047 by Tinkutara last updated on 10/Oct/17 $$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:\mathrm{the}\:\mathrm{4}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{2}\:+\:\frac{\mathrm{3}}{\mathrm{8}}{x}\right)^{\mathrm{10}} \:\mathrm{has}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}. \\ $$ Commented by Tinkutara last updated on 10/Oct/17…

1-2-3-1-4-5-6-1-7-8-9-

Question Number 153103 by amin96 last updated on 04/Sep/21 $$\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{5}\centerdot\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{7}\centerdot\mathrm{8}\centerdot\mathrm{9}}+\ldots \\ $$ Answered by puissant last updated on 04/Sep/21 $${S}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)\left(\mathrm{3}{n}+\mathrm{3}\right)} \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question-87553

Question Number 87553 by TawaTawa1 last updated on 05/Apr/20 Answered by ajfour last updated on 05/Apr/20 $${let}\:{no}.\:{of}\:{boys}\:{in}\:{A}=\mathrm{3}{k} \\ $$$$\:\:\:\:………..{girls}\:\:….\:{A}\:=\:\mathrm{2}{k} \\ $$$${let}\:\:{no}.\:{of}\:{girls}\:{in}\:{B}=\:{x} \\ $$$$\&\:\:\:{no}.\:{of}\:{boys}\:{in}\:{B}\:=\:{y} \\ $$$${no}.\:{of}\:{girls}\:{in}\:{C}\:=\:{z}…

Solve-the-equation-1-z-2z-2-1-2z-1-z-2-

Question Number 153079 by mathdanisur last updated on 04/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\sqrt{\mathrm{1}-\boldsymbol{{z}}}\:=\:\mathrm{2}\boldsymbol{{z}}^{\mathrm{2}} \:-\:\mathrm{1}\:+\:\mathrm{2}\boldsymbol{{z}}\:\sqrt{\mathrm{1}-\boldsymbol{{z}}^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 04/Sep/21 $$\mathrm{I}\:\mathrm{get}\:{z}=\mathrm{sin}\:\frac{\pi}{\mathrm{5}}\:=\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\…

Question-87533

Question Number 87533 by mr W last updated on 04/Apr/20 Commented by MJS last updated on 05/Apr/20 $${a}=\frac{\mathrm{49}}{\mathrm{76}}\pm\frac{\mathrm{457}\sqrt{\mathrm{87}}}{\mathrm{6612}} \\ $$$${b}=\frac{\mathrm{49}}{\mathrm{76}}\mp\frac{\mathrm{457}\sqrt{\mathrm{87}}}{\mathrm{6612}} \\ $$$${x}=−\mathrm{7}\pm\sqrt{\mathrm{87}} \\ $$$${y}=−\mathrm{7}\mp\sqrt{\mathrm{87}} \\…

i-still-search-about-a-general-and-complete-solution-about-this-determine-x-in-N-where-7-divise-2-x-3-x-note-it-is-just-an-exercise-in-secondary-so-dont-go-away-maybe-we-must-use-separation-of

Question Number 21990 by hi147 last updated on 08/Oct/17 $${i}\:{still}\:{search}\:{about}\:{a}\:{general}\:{and}\: \\ $$$${complete}\:{solution}\:{about}\:{this} \\ $$$${determine}\:{x}\:{in}\:{N}\:{where}\:\mathrm{7}\:{divise}\:\mathrm{2}^{{x}} +\mathrm{3}^{{x}} \\ $$$${note}\:=\:{it}\:{is}\:{just}\:{an}\:{exercise}\:{in}\:{secondary} \\ $$$${so}\:{dont}\:{go}\:{away}… \\ $$$${maybe}\:{we}\:{must}\:{use}\:{separation}\:{of}\:{cases} \\ $$$${methode}…. \\ $$…

Question-153046

Question Number 153046 by Tawa11 last updated on 04/Sep/21 Commented by Tawa11 last updated on 04/Sep/21 $$\mathrm{If}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{x}\:\:\mathrm{and}\:\:\mathrm{y}\:\:\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{system}\:\mathrm{shown},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{3}} \:\:\:+\:\:\:\mathrm{y}^{\mathrm{3}} \\ $$ Answered by mr…