Question Number 25457 by Tinkutara last updated on 10/Dec/17 Answered by prakash jain last updated on 10/Dec/17 $${n}^{\mathrm{2}} +{n}+\mathrm{1}={an}\left({n}−\mathrm{1}\right)+{bn}+{c} \\ $$$${n}\left({n}−\mathrm{1}\right)+\mathrm{2}{n}+\mathrm{1} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{i}}…
Question Number 156513 by cortano last updated on 12/Oct/21 $$\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{3}} −\mathrm{26x}^{\mathrm{2}} −\mathrm{20x}+\mathrm{25}=\mathrm{0} \\ $$$$\mathrm{x}=?\:\left(\mathrm{exact}\:\mathrm{form}\right) \\ $$ Commented by john_santu last updated on 12/Oct/21 $$\Rightarrow{x}^{\mathrm{2}}…
Question Number 25444 by math solver last updated on 10/Dec/17 Commented by Rasheed.Sindhi last updated on 16/Dec/17 $$\bar {\mathrm{z}}+\mathrm{1}=\mathrm{iz}^{\mathrm{2}} +\mid\mathrm{z}\mid^{\mathrm{2}} \\ $$$$\mathrm{z}=\mathrm{x}+\mathrm{iy}\Rightarrow\overline {\mathrm{x}+\mathrm{iy}}+\mathrm{1}=\mathrm{i}\left(\mathrm{x}+\mathrm{iy}\right)^{\mathrm{2}} +\mid\mathrm{x}+\mathrm{iy}\mid \\…
Question Number 156507 by MathSh last updated on 11/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156502 by MathSh last updated on 11/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{integers}: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \right)\:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{6}} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 25425 by Tinkutara last updated on 10/Dec/17 $$\mathrm{Sum}\:\mathrm{of}\:\mathrm{series}\:\mathrm{1}\:+\:\mathrm{2}{x}\:+\:\mathrm{7}{x}^{\mathrm{2}} \:+\:\mathrm{20}{x}^{\mathrm{3}} \:+\:… \\ $$$$\mathrm{up}\:\mathrm{to}\:{n}\:\mathrm{terms}\:\mathrm{when}\:{x}\:=\:−\mathrm{1}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156485 by MathSh last updated on 11/Oct/21 $$\mathrm{2021}!\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\mathrm{2022}} {\prod}}\left(\mathrm{n}\:+\:\mathrm{k}\:+\:\mathrm{m}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{A}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{\mathrm{A}} \\ $$ Terms of Service Privacy Policy…
Question Number 90946 by Cynosure last updated on 27/Apr/20 $${determine}\:{x},{y},{z}\:\in\:\mathbb{R}\:{such}\:{that}\: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{z}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{2}{y}−\mathrm{2}{xy}+\mathrm{2}{xz}−\mathrm{16}{z}+\mathrm{35}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156482 by MathSh last updated on 11/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{3}\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:=\:\mathrm{4sin}\left(\mathrm{x}\:+\:\frac{\pi}{\mathrm{4}}\right) \\ $$ Answered by mr W last updated on 11/Oct/21 $$\mathrm{3}+\mathrm{sin}\:\left(\mathrm{2}{x}\right)=\mathrm{2}\sqrt{\mathrm{2}}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right) \\ $$$$\mathrm{9}+\mathrm{6sin}\:\left(\mathrm{2}{x}\right)+\mathrm{sin}^{\mathrm{2}}…
Question Number 156473 by DysAndroid last updated on 11/Oct/21 Answered by Rasheed.Sindhi last updated on 11/Oct/21 $$\frac{{x}−\mathrm{6}}{\mathrm{2}}+\frac{{x}−\mathrm{7}}{\mathrm{2}}=\frac{\mathrm{2}{x}+\mathrm{7}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}−\mathrm{13}=\mathrm{2}{x}+\mathrm{7} \\ $$$$\:\:\:\:−\mathrm{13}=\mathrm{7} \\ $$$${No}\:{solution} \\ $$…