Category: Arithmetic

Question Number 207731 by efronzo1 last updated on 24/May/24 $$\downharpoonleft \underset{―}{}$$ Answered by A5T last updated on 24/May/24 Commented by A5T last updated on…

Question Number 207546 by pete last updated on 18/May/24 $$\mathrm{The}\mathrm{real}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{equation}{\mathrm{x}}^2+6\mathrm{x}+\mathrm{c}=0$$$$\mathrm{differ}\mathrm{by}2\mathrm{n},\mathrm{where}\mathrm{n}\mathrm{is}\mathrm{a}\mathrm{real}\mathrm{non}-\mathrm{zero}.$$$$\mathrm{Show}\mathrm{that}{\mathrm{n}}^2=9-\mathrm{c}$$$$\mathrm{Given}\mathrm{that}\mathrm{the}\mathrm{roots}\mathrm{also}\mathrm{have}\mathrm{opposite}$$$$\mathrm{signs},\mathrm{find}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{possible}\mathrm{values}\mathrm{of}\mathrm{n}$$ Answered by A5T…

Question Number 207194 by sniper237 last updated on 09/May/24 $$Letx=cos\frac{\pi }{9}$$$$Showthat8x^3-6x-1=0$$$$Deducexisnotrational$$ Answered by Berbere last updated on 09/May/24 $${cos}\left(\mathrm{3}.\frac{\pi}{\mathrm{9}}\right)={cos}\left(\frac{\pi}{\mathrm{3}}\right)=\frac{\mathrm{1}}{\mathrm{2}}…

Question Number 206924 by mr W last updated on 01/May/24 Commented by mr W last updated on 01/May/24 $$x,y,z\in \mathbb{N}$$ Answered by MATHEMATICSAM last…

Question Number 206848 by BaliramKumar last updated on 27/Apr/24 Commented by BaliramKumar last updated on 27/Apr/24 Answered by A5T last updated on 27/Apr/24 $${Let}\:{side}\:{of}\:{square}={s} \…