Question Number 151205 by EDWIN88 last updated on 19/Aug/21 $$\underbrace{ }\:\begin{array}{|c|c|}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} +\mathrm{1}\:=\left(\mathrm{2}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} }\\{{x}\:=?\:}\\\hline\end{array} \\ $$ Answered by bramlexs22 last updated on 19/Aug/21 $$\:\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{x}} }\:+\:\mathrm{1}\:=\:\frac{\mathrm{2}^{\mathrm{x}} }{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\frac{\mathrm{x}}{\mathrm{2}}}…
Question Number 151211 by EDWIN88 last updated on 19/Aug/21 $$\:{Find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{9}} \: \\ $$$${from}\:{expression}\: \\ $$$$\:\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{4}} \right)\left(\mathrm{1}+\mathrm{5}{x}^{\mathrm{5}} \right)…\left(\mathrm{1}+\mathrm{10}{x}^{\mathrm{10}} \right) \\ $$ Answered by Olaf_Thorendsen…
Question Number 85664 by Jidda28 last updated on 23/Mar/20 $$\boldsymbol{{S}\mathrm{how}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{order}}\:\mathrm{100}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{not}}\:\boldsymbol{\mathrm{simple}} \\ $$ Commented by mind is power last updated on 24/Mar/20 $$\mathrm{100}=\mathrm{2}^{\mathrm{2}} .\mathrm{5}^{\mathrm{2}} \\ $$$${let}\:{see}\:{sylow}\:{Theorem}…
Question Number 151192 by mathdanisur last updated on 18/Aug/21 Commented by liberty last updated on 19/Aug/21 $$\mathrm{q151198} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 151198 by liberty last updated on 19/Aug/21 $$\mathrm{If}\:{a},\mathrm{b}\in\mathrm{R}\:\mathrm{satisfy}\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} −\mathrm{6}{a}^{\mathrm{2}} {b}^{\mathrm{2}} =\mathrm{9}\:{and} \\ $$$${ab}\left({a}−{b}\right)\left({a}+{b}\right)=−\mathrm{11}\:\mathrm{then}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =? \\ $$ Answered by EDWIN88 last updated…
Question Number 151189 by mathdanisur last updated on 18/Aug/21 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}:\:\left(\boldsymbol{\varphi}-\mathrm{golden}\:\mathrm{ratio}\right) \\ $$$$\mathrm{sinA}\:+\:\frac{\mathrm{sinB}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{sinC}}{\boldsymbol{\varphi}}\:<\:\frac{\mathrm{1}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{1}+\sqrt{\boldsymbol{\varphi}}+\boldsymbol{\varphi}}{\mathrm{2}\boldsymbol{\varphi}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20118 by Tinkutara last updated on 22/Aug/17 $$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{equations}\:{x}^{\mathrm{2}} \:−\:\mathrm{6}{x}\:+\:{a}\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} \:−\:{cx}\:+\:\mathrm{6}\:=\:\mathrm{0}\:\mathrm{have}\:\mathrm{one}\:\mathrm{root}\:\mathrm{in} \\ $$$$\mathrm{common}.\:\mathrm{The}\:\mathrm{other}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{and}\:\mathrm{second}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{integers}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}\::\:\mathrm{3}.\:\mathrm{Then},\:\mathrm{find}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{root}. \\ $$ Answered…
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Question Number 20116 by Tinkutara last updated on 22/Aug/17 $$\mathrm{If}\:{a}\:\mathrm{and}\:{b}\:\left(\neq\:\mathrm{0}\right)\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:\left({x}\:\in\:{R}\right). \\ $$ Answered by ajfour last updated on 22/Aug/17…
Question Number 151191 by mathdanisur last updated on 18/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com