Category: Algebra

Question Number 12927 by satish1992.mishra@gmail.com last updated on 07/May/17 $$\mathrm{\Sigma }\cos \left(\frac{1}{n}\right)$$ Commented by prakash jain last updated on 07/May/17 $$nfrom0to\mathrm{\infty }?$$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:\left(\frac{\mathrm{1}}{{n}}\right)?…

Question Number 78449 by mathocean1 last updated on 17/Jan/20 $$\mathrm{find}\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{definition}\mathrm{of}$$$$\mathrm{f}\left(x\right)=\frac{-x}{\mid x\mid -x}$$ Commented by Rio Michael last updated on 18/Jan/20 $$f\left(x\right)=\frac{x}{x-\mid x\mid }$$$${so}\:{x}\:<\:\mathrm{0}\:{so}\:{that}\:{x}−\mid{x}\mid\:{should}\:{be}\:…

Question Number 12909 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17 Answered by nume1114 last updated on 07/May/17 $$a^2(a+1)+b^2(b+1)+5ab$$$$={a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{5}{ab}…

Question Number 143979 by mathdanisur last updated on 20/Jun/21 Answered by mitica last updated on 20/Jun/21 $$p=x+y+z;q=xy+yz+xz;r=xyz\Rightarrow p^2⩾3q$$$$3{(p+\frac{3r}{q})}^4=3{(\frac{p}{3}+\frac{p}{3}+\frac{p}{3}+\frac{3r}{q})}^4\stackrel{am-gm}{⩾}$$$$\geqslant\mathrm{3}\left(\mathrm{4}\centerdot\sqrt[{\mathrm{4}}]{\frac{{p}}{\mathrm{3}}\centerdot\frac{{p}}{\mathrm{3}}\centerdot\frac{{p}}{\mathrm{3}}\centerdot\frac{\mathrm{3}{r}}{{q}}}\right)^{\mathrm{4}}…

Question Number 12889 by sin (x) last updated on 05/May/17 $$f(x-1)=\frac{2}{3}+f\left(x\right)$$$$f\left(0\right)=36-f\left(21\right)$$$$\Rightarrow f\left(0\right)=?$$ Commented by prakash jain last updated on 06/May/17…