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}} \\ $$$$\mathrm{2}{x}−\mathrm{13}=\mathrm{2}{x}+\mathrm{7} \\ $$$$\:\:\:\:−\mathrm{13}=\mathrm{7} \\ $$$${No}\:{solution} \\ $$…
Question Number 156467 by MathSh last updated on 11/Oct/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{4xyz}+\mathrm{4xy}+\mathrm{2yz}+\mathrm{3zx}=\mathrm{6} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{2x}+\mathrm{3y}+\mathrm{4z}\:\geqslant\:\mathrm{4}\left(\mathrm{xy}+\mathrm{yz}+\mathrm{zx}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156463 by MathSh last updated on 11/Oct/21 $$\mathrm{Find}: \\ $$$$\mathrm{f}\::\:\mathbb{N}^{\ast} \:\rightarrow\:\mathbb{N}^{\ast} \:\:;\:\:\:\mathrm{2}\left(\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{y}\right)\right)\:=\:\mathrm{x} \\ $$$$\forall\mathrm{x}\in\mathbb{N}^{\ast} \\ $$ Answered by FongXD last updated on 11/Oct/21…
Question Number 25390 by sand33pkuma4@gmail.com last updated on 09/Dec/17 $$\mathrm{sin}\:\mathrm{90} \\ $$ Answered by Rasheed.Sindhi last updated on 09/Dec/17 $$\mathrm{sin}\:\mathrm{2}\theta=\mathrm{2}\:\mathrm{sin}\theta\:\mathrm{cos}\theta \\ $$$$\mathrm{sin}\:\mathrm{90}=\mathrm{sin}\left(\mathrm{2}×\mathrm{45}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\:\mathrm{sin}\:\mathrm{45}\:\mathrm{cos}\:\mathrm{45} \\…
Question Number 156462 by MathSh last updated on 11/Oct/21 $$\mathrm{If}\:\:\:\overline {\mathrm{abc}}\:=\:\overline {\mathrm{cba}}\:+\:\overline {\mathrm{def}}\:\:\mathrm{and}\:\:\mathrm{a}\in\left\{\mathrm{c}+\mathrm{2};…;\mathrm{9}\right\} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\:\:\overline {\mathrm{def}}\:+\:\overline {\mathrm{fed}}\: \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last…