Question Number 29805 by mrW2 last updated on 12/Feb/18 $${f}\left({x}\right)=\left({x}+{a}_{\mathrm{1}} \right)\left({x}+{a}_{\mathrm{2}} \right)\left({x}+{a}_{\mathrm{3}} \right)…\left({x}+{a}_{{n}} \right) \\ $$$${find}\:{the}\:{coefficient}\:{of}\:{term}\:{x}^{{k}} \:\left(\mathrm{0}\leqslant{k}\leqslant{n}\right) \\ $$ Commented by mrW2 last updated on…
Question Number 160869 by HongKing last updated on 08/Dec/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$ Commented by smallEinstein last updated on 10/Dec/21 Commented…
Question Number 160871 by cortano last updated on 08/Dec/21 $$\:\:\sqrt[{\mathrm{6}}]{\left(\mathrm{2}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}\sqrt{\mathrm{13}}+\mathrm{5}}{\:\sqrt{\mathrm{5}}+\mathrm{2}}}\:+\mathrm{2}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}\sqrt{\mathrm{13}}−\mathrm{5}}{\:\sqrt{\mathrm{5}}−\mathrm{2}}}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}}=? \\ $$ Answered by MJS_new last updated on 08/Dec/21 $$\left(\pm\mathrm{5}+\mathrm{2}\sqrt{\mathrm{13}}\right)^{\mathrm{1}/\mathrm{3}} =\pm\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{13}}}{\mathrm{2}} \\ $$$$\left(\pm\mathrm{2}+\sqrt{\mathrm{5}}\right)^{\mathrm{1}/\mathrm{3}} =\pm\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}…
Question Number 160867 by cortano last updated on 08/Dec/21 $$ \\ $$A piece of metal in the form of an equilateral triangle that has been…
Question Number 95328 by mr W last updated on 24/May/20 Commented by mr W last updated on 24/May/20 $${reposted}\:{question} \\ $$ Commented by MJS last…
Question Number 95324 by I want to learn more last updated on 24/May/20 $$\mathrm{If}\:\:\:\mathrm{sin}\:\mathrm{A}\:\:+\:\:\left(\mathrm{sin}\:\mathrm{A}\right)^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1} \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{12}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{10}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{8}} \:\:+\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{6}} \:\:−\:\:\mathrm{1}\:\:\:\:\:\mathrm{is}\:? \\ $$$$…
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Question Number 160853 by HongKing last updated on 07/Dec/21 Commented by HongKing last updated on 08/Dec/21 $$\mathrm{Answer}:\:\:\sqrt{\mathrm{106}} \\ $$ Answered by kowalsky78 last updated on…
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Question Number 29777 by Joel578 last updated on 12/Feb/18 $${f}\left({x}\right)\:=\:\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right)…\left({x}\:−\:\mathrm{50}\right) \\ $$$$\mathrm{Find}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{49}} \\ $$ Commented by mrW2 last updated on 12/Feb/18 $${see}\:{Q}\mathrm{29805} \\ $$ Commented…