Category: Algebra

Question Number 158774 by HongKing last updated on 08/Nov/21 Answered by MJS_new last updated on 08/Nov/21 $$\mathrm{sin}^{\mathrm{4}} \:{x}\:+\mathrm{cos}^{\mathrm{2}} \:{x}\:=\mathrm{sin}^{\mathrm{2}} \:{x}\:+\mathrm{cos}^{\mathrm{4}} \:{x} \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{2}\sqrt{\mathrm{7}+\mathrm{cos}\:\mathrm{4}{x}}+\sqrt{\mathrm{9}−\mathrm{cos}\:\mathrm{4}{x}}=\mathrm{6}\sqrt{\mathrm{2}}…

Question Number 158759 by HongKing last updated on 08/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\mathrm{2}\boldsymbol{\mathrm{n}}} {\sum}}\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{k}}} \:\centerdot\:\frac{\mathrm{4n}\:+\:\mathrm{1}}{\mathrm{4n}\:-\:\mathrm{2k}\:+\:\mathrm{1}}\begin{pmatrix}{\mathrm{2n}}\\{\:\mathrm{k}}\end{pmatrix}}\:=\:\mathrm{1} \\ $$$$ \\ $$ Answered by mindispower last updated…

Question Number 27662 by abdo imad last updated on 12/Jan/18 $${factorize}\:{in}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\:+{z}^{\mathrm{2}} \:\:.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158721 by HongKing last updated on 08/Nov/21 $$\mathrm{Find}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{1}\:+\:\mathrm{ax}\right)}\:\mathrm{dx}\:\:;\:\:\mathrm{a}>\mathrm{0} \\ $$$$ \\ $$ Answered by ajfour last updated on…

Question Number 93177 by ar247 last updated on 11/May/20 $${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{47} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\:\sqrt{{x}}}=… \\ $$ Commented by ar247 last updated on 11/May/20 $${help} \\…