Category: Algebra

Question Number 125428 by ajfour last updated on 11/Dec/20 Commented by ajfour last updated on 11/Dec/20 $$Findequationofcirclepassing$$$$through(1,1)andP(p,p^2)with$$$$radiust<1/2.$$ Terms…

Question Number 190942 by mathlove last updated on 14/Apr/23 $$(x+y)(x^2-xy+y^2)=2$$$$\frac{x^3{y}^3}{x^9+y^9-8}=?$$ Answered by Frix last updated…

Question Number 190938 by Shrinava last updated on 14/Apr/23 Answered by Frix last updated on 15/Apr/23 $$\tan 3x-\tan x\tan 11x\tan 13x=0$$$$\mathrm{We}\mathrm{can}\mathrm{transform}\mathrm{this}\mathrm{to}$$$$\sin 28x-\sin 20x+\sin 4x=0$$$$y=4x$$$$\mathrm{sin}\:\mathrm{7}{y}\:−\mathrm{sin}\:\mathrm{5}{y}\:+\mathrm{sin}\:{y}\:=\mathrm{0}…

Question Number 190916 by Abdullahrussell last updated on 14/Apr/23 Commented by Rasheed.Sindhi last updated on 14/Apr/23 $$6A+12B+24C=100$$$$6\mid (6A+12B+24C)\wedge 6\nmid 100$$$$\Rightarrow \nexists integersolution!$$ Terms of…

Question Number 59833 by bhanukumarb2@gmail.com last updated on 15/May/19 Answered by tanmay last updated on 15/May/19 $$e^{i\theta }=cos\theta +isin\theta$$$$e^{-i\theta }=cos\theta -isin\theta$$$${cos}\theta=\frac{{e}^{{i}\theta} +{e}^{−{i}\theta} }{\mathrm{2}}\rightarrow{cosi}=\frac{{e}^{−\mathrm{1}}…