Question Number 138594 by Ar Brandon last updated on 15/Apr/21 Commented by Ar Brandon last updated on 15/Apr/21 $$\mathrm{In}\:\mathrm{honour}\:\mathrm{of}\:\mathrm{Leonhard}\:\mathrm{Euler} \\ $$$$\mathrm{on}\:\mathrm{his}\:\mathrm{314}^{\mathrm{th}} \:\mathrm{anniversary}. \\ $$ Commented…
Question Number 73057 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} =\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} −{x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1} \\ $$$${prove}\:{that}\:{x}^{\mathrm{2}} \:+{x}\:{divide}\:\underset{{n}} {{P}} \\ $$ Answered by MJS last…
Question Number 7519 by Tawakalitu. last updated on 01/Sep/16 $${A}\:\left(\mathrm{2}\:×\:\mathrm{3}\right)\:{rectangle}\:{and}\:{a}\:\left(\mathrm{3}\:×\:\mathrm{4}\right)\:{rectangle}\:{are}\:{contain}\:{within}\: \\ $$$${a}\:{square}\:{without}\:{over}\:{laping}\:{at}\:{any}\:{inferior}\:{point}\:,\:{and}\:{the}\: \\ $$$${sides}\:{of}\:{the}\:{square}\:{are}\:{parallel}\:{to}\:{the}\:{sides}\:{of}\:{the}\:{two}\:{given} \\ $$$${rectangles}.\:{what}\:{is}\:{the}\:{smallest}\:{possible}\:{area}\:{of}\:{the}\:{square}. \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 73055 by mathmax by abdo last updated on 05/Nov/19 $${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction}\:\:\frac{{x}^{\mathrm{4}} \:+{x}+\mathrm{1}}{{x}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73052 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} ={X}^{{n}} \:+{X}^{{n}−\mathrm{1}} \:+….+{X}^{\mathrm{2}} \:+{X}−\mathrm{1}\:\in{R}\left[{X}\right] \\ $$$$\left.\mathrm{1}\left.\right){prove}\:{that}\:{P}_{{n}} {have}\:{one}\:{root}\:{x}_{{n}} \:{inside}\:\right]\mathrm{0},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{sequence}\:{x}_{{n}} \\ $$ Answered…
Question Number 73051 by mathmax by abdo last updated on 05/Nov/19 $${factorize}\:{inside}\:{R}\left[{X}\right] \\ $$$$\left.\mathrm{1}\right){X}^{\mathrm{5}} −\mathrm{1}\:\: \\ $$$$\left.\mathrm{2}\right){X}^{\mathrm{6}} \:+\mathrm{1} \\ $$ Commented by mathmax by abdo…
Question Number 7514 by Tawakalitu. last updated on 01/Sep/16 Answered by Yozzia last updated on 01/Sep/16 $${sin}\left(\pi{cos}\alpha\right)={cos}\left(\pi{sin}\alpha\right). \\ $$$${Using}\:{sina}={cos}\left(\frac{\pi}{\mathrm{2}}−{a}\right),\:{we}\:{get} \\ $$$${cos}\left(\frac{\pi}{\mathrm{2}}−\pi{cos}\alpha\right)={cos}\left(\pi{sin}\alpha\right) \\ $$$$\Rightarrow\frac{\pi}{\mathrm{2}}−\pi{cos}\alpha=\mathrm{2}{n}\pi\pm\pi{sin}\alpha\:\:\:\:\left({n}\in\mathbb{Z}\right) \\ $$$$\mp\pi{sin}\alpha−\pi{cos}\alpha=\mathrm{2}{n}\pi−\frac{\pi}{\mathrm{2}}…
Question Number 73048 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{Z}^{\mathrm{2}} \:\:{x}^{\mathrm{2}} \:+\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} \:=\mathrm{122} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73049 by mathmax by abdo last updated on 05/Nov/19 $${simplifyA}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(\frac{{k}}{{n}}−\alpha\right)^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{X}^{{k}} \left(\mathrm{1}−{X}\right)^{{n}−{k}} \\ $$ Terms of Service Privacy…
Question Number 73046 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\forall{n}\:\in{N}\:\:\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:{C}_{\mathrm{2}{n}} ^{{n}+{k}} \:={nC}_{\mathrm{2}{n}−\mathrm{1}} ^{{n}} \\ $$ Answered by mind is power last…