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Category: Algebra

solve-inside-N-2-x-1-y-2-2xy-

Question Number 61650 by maxmathsup by imad last updated on 05/Jun/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\:\left({x}+\mathrm{1}\right)\left({y}+\mathrm{2}\right)\:=\mathrm{2}{xy} \\ $$ Commented by kaivan.ahmadi last updated on 06/Jun/19 $${xy}+\mathrm{2}{x}+{y}+\mathrm{2}−\mathrm{2}{xy}=\mathrm{0} \\ $$$${xy}=\mathrm{2}{x}+{y}+\mathrm{2}…

Find-the-value-of-9x-1-100-x-3-9x-2-100-x-3-9x-3-100-x-3-9x-2013-100-x-3-

Question Number 192697 by cortano12 last updated on 25/May/23 $$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} …\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$ Answered by AST last updated on 31/May/23…

Prove-that-C-n-k-1-2pi-pi-pi-2cos-2-n-cos-n-2-k-d-

Question Number 192688 by Erico last updated on 24/May/23 $$\mathrm{Prove}\:\mathrm{that}\:: \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \:=\:\frac{\mathrm{1}}{\mathrm{2}\pi}\:\underset{\:−\pi} {\int}^{\:\:\:\pi} \left(\mathrm{2cos}\frac{\theta}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{cos}\left[\left(\frac{\mathrm{n}}{\mathrm{2}}−\mathrm{k}\right)\theta\right]\mathrm{d}\theta \\ $$ Answered by witcher3 last updated on…

Find-x-1-lg-5x-2-6-lg-5x-6-0-2-2x-5-log-3-1-5-x-0-3-4-x-14-2-x-32-0-

Question Number 192676 by Shrinava last updated on 24/May/23 $$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\:\mathrm{lg}\left(\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{6}\right)\centerdot\mathrm{lg}\left(\mathrm{5x}\:−\:\mathrm{6}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{2}.\:\:\left(\mathrm{2x}\:−\:\mathrm{5}\right)\centerdot\mathrm{log}_{\mathrm{3}} \left(\mathrm{1},\mathrm{5}\:−\:\mathrm{x}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{3}.\:\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{14}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{32}\:=\:\mathrm{0} \\ $$ Answered by Frix…