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Category: Algebra

Find-2-2-2-2-2-2-2-2-2-

Question Number 160445 by HongKing last updated on 29/Nov/21 $$\mathrm{Find}: \\ $$$$\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\:\centerdot\:\frac{\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}}{\mathrm{2}}\:\centerdot\:\frac{\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}}}{\mathrm{2}}\:\centerdot\:…\:=\:? \\ $$ Commented by HongKing last updated on 29/Nov/21 $$\mathrm{Yes}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{Sir}\:\mathrm{but}\:\mathrm{how}\:\mathrm{please} \\ $$ Commented…

Find-lim-x-2-1-x-1-pi-x-x-3-8-

Question Number 160444 by HongKing last updated on 29/Nov/21 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{x}}\:+\:\mathrm{1}\right)\:-\:\frac{\sqrt{\pi}}{\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{8}}\:=\:? \\ $$ Answered by Ar Brandon last updated on 29/Nov/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\Gamma\left(\frac{\mathrm{1}}{{x}}+\mathrm{1}\right)−\frac{\sqrt{\pi}}{{x}}}{{x}^{\mathrm{3}} −\mathrm{8}}…

Question-160424

Question Number 160424 by cortano last updated on 29/Nov/21 Answered by MJS_new last updated on 29/Nov/21 $$\mathrm{let}\:{y}={px}\:\Rightarrow \\ $$$$\begin{cases}{{x}\left(\left({p}^{\mathrm{4}} −\mathrm{1}\right){x}^{\mathrm{3}} −{p}+\mathrm{2}\right)=\mathrm{0}}\\{\left({p}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} {x}^{\mathrm{6}} +\mathrm{3}=\mathrm{0}}\end{cases} \\…

Question-94874

Question Number 94874 by i jagooll last updated on 21/May/20 Commented by hknkrc46 last updated on 21/May/20 $$\sqrt{\mathrm{2}−\mathrm{7x}}+\mathrm{2x}=\mathrm{0} \\ $$$$\bigstar\:\sqrt[{\mathrm{2n}}]{\mathrm{f}\left(\mathrm{x}\right)}\geqslant\mathrm{0}\:\:\wedge\:\mathrm{f}\left(\mathrm{x}\right)\geqslant\mathrm{0}\:;\:\mathrm{n}\in\mathbb{Z}^{+} \\ $$$$\bigstar\:\mathrm{n}=\mathrm{1}\:\Rightarrow\:\sqrt[{\mathrm{2}}]{\mathrm{f}\left(\mathrm{x}\right)}=\sqrt{\mathrm{f}\left(\mathrm{x}\right)} \\ $$$$\Rightarrow\:\sqrt{\mathrm{2}−\mathrm{7x}}=−\mathrm{2x} \\…

1-1-1-2-1-1-1-2-1-1-x-2-

Question Number 160405 by HongKing last updated on 29/Nov/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}+\frac{\mathrm{1}}{….}}}}}\:\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{2}} \:=\:? \\ $$ Commented by quvonnn last updated on 29/Nov/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{{x}}}={x} \\ $$$$\left({x}+\mathrm{2}\right)+{x}={x}\left({x}+\mathrm{2}\right) \\ $$$$\mathrm{2}{x}+\mathrm{2}={x}^{\mathrm{2}}…