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Category: Algebra

let-give-P-n-x-x-1-2n-x-2-n-1-and-Q-x-x-2-3x-2-find-R-x-P-n-x-R-x-Q-x-

Question Number 28312 by abdo imad last updated on 23/Jan/18 $${let}\:{give}\:\:{P}_{{n}} \left({x}\right)=\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}} \:+\left({x}+\mathrm{2}\right)^{{n}} −\mathrm{1}\:{and} \\ $$$${Q}\left({x}\right)=\:{x}^{\mathrm{2}} \:+\mathrm{3}{x}\:+\mathrm{2}\:\:{find}\:{R}\left({x}\right)\:/{P}_{{n}} \left({x}\right)={R}\left({x}\right)\:{Q}\left({x}\right)\:. \\ $$ Answered by sma3l2996 last updated…

let-S-x-n-0-3x-n-2-using-the-sum-above-find-n-0-1-n-1-3-n-1-n-3-

Question Number 159379 by HongKing last updated on 16/Nov/21 $$\mathrm{let}\:\:\boldsymbol{\mathrm{S}}\left(\mathrm{x}\right)\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\mathrm{3x}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{2}} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{above}\:\mathrm{find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \left(\mathrm{n}\:+\:\mathrm{3}\right)}\: \\ $$ Answered by Ar…

let-x-y-gt-0-such-that-x-3-y-3-2-find-the-minimum-value-of-the-following-expression-P-2020x-2021y-

Question Number 159378 by HongKing last updated on 16/Nov/21 $$\mathrm{let}\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{expression}: \\ $$$$\mathrm{P}\:=\:\mathrm{2020}\boldsymbol{\mathrm{x}}\:+\:\mathrm{2021}\boldsymbol{\mathrm{y}} \\ $$ Commented by mr W last…

Question-28288

Question Number 28288 by Mr eaay last updated on 23/Jan/18 Answered by Rasheed.Sindhi last updated on 23/Jan/18 $$\:^{\bullet} \left(\mathrm{2}+\sqrt{\mathrm{3}}\:\right)^{−\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{3}}}×\frac{\mathrm{2}−\sqrt{\mathrm{3}}}{\mathrm{2}−\sqrt{\mathrm{3}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\:\:^{\bullet} \left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}}…

Question-159355

Question Number 159355 by mnjuly1970 last updated on 16/Nov/21 Answered by mr W last updated on 16/Nov/21 $${radius}\:{of}\:{small}\:{circle}\:{r}=\frac{{b}}{\mathrm{2}} \\ $$$$\frac{{b}}{\mathrm{2}}×\frac{{b}}{\mathrm{2}}=\left({a}−\frac{{b}}{\mathrm{2}}\right)\left({a}+\frac{{b}}{\mathrm{2}}\right) \\ $$$$\frac{{b}^{\mathrm{2}} }{\mathrm{4}}={a}^{\mathrm{2}} −\frac{{b}^{\mathrm{2}} }{\mathrm{4}}…

let-give-the-polynomial-P-x-1-2i-1-ix-n-1-ix-n-find-the-roots-of-P-x-and-factorize-P-x-

Question Number 28267 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:{the}\:{polynomial} \\ $$$${P}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}{i}}\left(\:\left(\mathrm{1}+{ix}\right)^{{n}} \:−\left(\mathrm{1}−{ix}\right)^{{n}} \right)\:.{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$${and}\:{factorize}\:{P}\left({x}\right). \\ $$ Commented by abdo imad last updated…

1-find-P-R-x-P-sinx-sin-2n-1-x-2-find-the-roots-of-P-and-degP-3-decompose-1-P-and-prove-that-2n-1-sin-2n-1-x-k-0-2n-1-k-cos-kpi-2n-1-sinx-sin-kpi-2n-1

Question Number 28265 by abdo imad last updated on 22/Jan/18 $$\left.\mathrm{1}\right)\:\:{find}\:{P}\in{R}\left[{x}\right]\:/\:{P}\left({sinx}\right)\:={sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\:{and}\:{degP} \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:\:\frac{\mathrm{1}}{{P}}\:\:{and}\:{prove}\:{that} \\ $$$$\frac{\mathrm{2}{n}+\mathrm{1}}{{sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x}}\:=\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{k}} \:{cos}\left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)}{{sinx}−{sin}\:\left(\frac{{k}\pi}{\left.\mathrm{2}{n}+\mathrm{1}\right)}\right)}\:\:. \\ $$ Terms of Service…