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Category: Algebra

x-2-xy-x-y-2-y-2-xy-x-y-1-3x-y-

Question Number 148756 by mathdanisur last updated on 30/Jul/21 $$\begin{cases}{{x}^{\mathrm{2}} \:+\:{xy}\:+\:{x}\:+\:{y}\:=\:−\mathrm{2}}\\{{y}^{\mathrm{2}} \:+\:{xy}\:+\:{x}\:+\:{y}\:=\:\mathrm{1}}\end{cases}\:\:\Rightarrow\:\mathrm{3}{x}\:+\:{y}\:=\:? \\ $$ Answered by mindispower last updated on 30/Jul/21 $$\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\Rightarrow\left({x}+{y}\right)^{\mathrm{2}} +\mathrm{2}\left({x}+{y}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\left(\mathrm{1}+\left({x}+{y}\right)\right)^{\mathrm{2}}…

please-help-me-with-this-confusing-question-x-2x-y-y-y-x-4-1-xy-xy-yx-16-2-solve-for-x-and-y-

Question Number 17638 by chux last updated on 08/Jul/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{this} \\ $$$$\mathrm{confusing}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2x}/\mathrm{y}} ×\mathrm{y}^{\mathrm{y}/\mathrm{x}} =\mathrm{4}……\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\left(\mathrm{xy}\right)^{\mathrm{xy}+\mathrm{yx}} =\mathrm{16}…..\left(\mathrm{2}\right) \\ $$$$…

Question-148706

Question Number 148706 by mathdanisur last updated on 30/Jul/21 Answered by mindispower last updated on 30/Jul/21 $${sin}^{\mathrm{2}} \left({x}\right)=\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}} \\ $$$$\left({E}\right)\Leftrightarrow\mathrm{2}−\frac{\mathrm{1}}{\mathrm{2}}\left({cos}\left(\mathrm{6}{x}\right)+{cos}\left(\mathrm{8}{x}\right)+{cos}\left(\mathrm{12}{x}\right)+{cos}\left(\mathrm{14}{x}\right)\right)=\mathrm{2} \\ $$$$\Leftrightarrow{cos}\left(\mathrm{6}{x}\right)+{cos}\left(\mathrm{14}{x}\right)+{cos}\left(\mathrm{8}{x}\right)+{cos}\left(\mathrm{12}{x}\right)=\mathrm{0} \\ $$$$\Leftrightarrow\mathrm{2}{cos}\left(\mathrm{10}{x}\right){cos}\left(\mathrm{4}{x}\right)+\mathrm{2}{cos}\left(\mathrm{10}{x}\right){cos}\left(\mathrm{2}{x}\right)=\mathrm{0} \\…

Solve-for-equation-2tg-3x-3tg-2x-tg-2-2x-tg-3x-

Question Number 148707 by mathdanisur last updated on 30/Jul/21 $${Solve}\:{for}\:{equation}: \\ $$$$\mathrm{2}{tg}\left(\mathrm{3}{x}\right)\:-\:\mathrm{3}{tg}\left(\mathrm{2}{x}\right)\:=\:{tg}^{\mathrm{2}} \left(\mathrm{2}{x}\right)\:\centerdot\:{tg}\left(\mathrm{3}{x}\right) \\ $$ Answered by nimnim last updated on 30/Jul/21 $${Let}\:{me}\:{give}\:{a}\:{try}…. \\ $$$$\Rightarrow\mathrm{2}\left(\frac{\mathrm{3}{tanx}−{tan}^{\mathrm{3}}…

lim-n-0-1-nx-1-n-2-x-4-dx-

Question Number 148655 by mathdanisur last updated on 29/Jul/21 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{{nx}}{\mathrm{1}\:+\:{n}^{\mathrm{2}} {x}^{\mathrm{4}} }\:{dx}\:=\:? \\ $$ Answered by ArielVyny last updated on 29/Jul/21 $${n}\int_{\mathrm{0}}…