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Question Number 154497 by mathdanisur last updated on 18/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\:\:\mathrm{2}\:\sqrt{\mathrm{2x}^{\mathrm{3}} \:-\:\mathrm{x}}\:=\:\mathrm{3x}^{\mathrm{2}} \:-\:\mathrm{3x}\:+\:\mathrm{2} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\:\:\sqrt{\frac{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{16}}{\mathrm{2}}}\:+\:\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4}\right)}\:=\:\mathrm{3x}\:+\:\mathrm{2} \\ $$ Answered by ARUNG_Brandon_MBU last updated…
Question Number 154493 by mathdanisur last updated on 18/Sep/21 $$\mathrm{If}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{then}: \\ $$$$\frac{\mathrm{a}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:+\:\mathrm{c}^{\mathrm{2}\boldsymbol{\mathrm{n}}} }{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \mathrm{b}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{n}}} \mathrm{c}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{c}^{\boldsymbol{\mathrm{n}}} \mathrm{a}^{\boldsymbol{\mathrm{n}}} }\:\geqslant\:\frac{\sqrt{\mathrm{3}\centerdot\left(\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \right)}}{\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}}…
Question Number 154495 by mathdanisur last updated on 18/Sep/21 $$\mathrm{if}\:\:\mathrm{S}_{\boldsymbol{\mathrm{n}}} \left(\mathrm{t}\right)\:=\:\mathrm{n}^{\mathrm{1}-\boldsymbol{\mathrm{t}}} \:\left(\frac{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}\boldsymbol{\mathrm{t}}} }{\left(\sqrt[{\boldsymbol{\mathrm{n}}+\mathrm{1}}]{\left(\mathrm{n}+\mathrm{1}\right)!}\right)^{\boldsymbol{\mathrm{t}}} }\:-\:\frac{\mathrm{n}^{\mathrm{2}\boldsymbol{\mathrm{t}}} }{\left(\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{n}!}\right)^{\boldsymbol{\mathrm{t}}} }\right) \\ $$$$\mathrm{with}\:\:\mathrm{t}>\mathrm{0} \\ $$$$\mathrm{then}\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}S}_{\boldsymbol{\mathrm{n}}} \left(\mathrm{t}\right)\:=\:\mathrm{te}^{\boldsymbol{\mathrm{t}}} \\ $$ Answered…
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Question Number 88921 by M±th+et£s last updated on 13/Apr/20 $${find}\:{x},{y} \\ $$$${x}−\mathrm{2}{y}−\sqrt{{xy}}=\mathrm{0} \\ $$$$\sqrt{{x}−\mathrm{1}}−\sqrt{\mathrm{2}{y}−\mathrm{1}}=\mathrm{1} \\ $$ Answered by behi83417@gmail.com last updated on 14/Apr/20 $$\begin{cases}{\left(\mathrm{x}−\mathrm{2y}\right)^{\mathrm{2}} =\mathrm{xy}\Rightarrow\mathrm{x}^{\mathrm{2}}…
Question Number 154458 by mathdanisur last updated on 18/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 18/Sep/21 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{sin}^{\mathrm{2}} {x}}{dx}=−{x}^{\mathrm{2}} \mathrm{cot}{x}+\mathrm{2}\int{x}\mathrm{cot}{xdx} \\ $$$$=−{x}^{\mathrm{2}} \mathrm{cot}{x}+\mathrm{2}{x}\mathrm{ln}\left(\mathrm{sin}{x}\right)−\mathrm{2}\int\mathrm{ln}\left(\mathrm{sin}{x}\right){dx} \\ $$$$\int_{\mathrm{0}}…
Question Number 154444 by Rasheed.Sindhi last updated on 18/Sep/21 Commented by Rasheed.Sindhi last updated on 18/Sep/21 $$\mathrm{Question}#\mathrm{154100}\:\:\mathrm{Reposted} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 154429 by liberty last updated on 18/Sep/21 Commented by liberty last updated on 18/Sep/21 $$ \\ $$$$\:{A}=\sqrt[{\mathrm{3}}]{−\mathrm{15}+\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}}+\sqrt[{\mathrm{3}}]{−\mathrm{15}−\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}} \\ $$$$ \\ $$ Commented by…
Question Number 23357 by Tinkutara last updated on 29/Oct/17 $${Prove}\:{that}\:\frac{\mathrm{1}}{{m}!}{C}_{\mathrm{0}} +\frac{{n}}{\left({m}+\mathrm{1}\right)!}{C}_{\mathrm{1}} +\frac{{n}\left({n}−\mathrm{1}\right)}{\left({m}+\mathrm{2}\right)!}{C}_{\mathrm{2}} \\ $$$$+…+\frac{{n}\left({n}−\mathrm{1}\right)…\mathrm{2}.\mathrm{1}}{\left({m}+{n}\right)!}{C}_{{n}} = \\ $$$$\frac{\left({m}+{n}+\mathrm{1}\right)\left({m}+{n}+\mathrm{2}\right)…\left({m}+\mathrm{2}{n}\right)}{\left({m}+{n}\right)!}. \\ $$ Terms of Service Privacy Policy Contact:…