Category: Algebra

Question Number 210508 by hardmath last updated on 11/Aug/24 Answered by mr W last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24…

Question Number 210496 by lmcp1203 last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24 $$hasthatbracketaspecialmeaning?$$ Commented by lmcp1203 last updated…

Question Number 210439 by universe last updated on 09/Aug/24 Commented by universe last updated on 09/Aug/24 $$provethatthesequenceisboundedand$$$$convergent$$ Answered by aleks041103 last…

Question Number 210362 by MATHEMATICSAM last updated on 10/Sep/24 $$\mathrm{If}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{quadratic}\mathrm{equation}$$$$(a-b+c)x^2+(c-b-a)x+2(b-c)=0$$$$\mathrm{are}\mathrm{real}\mathrm{and}\mathrm{equal}\mathrm{then}\mathrm{find}\frac{a}{b-c}.$$ Commented by som(math1967) last updated on 08/Aug/24 $${not}\:{qudratic}\:,{it}\:{should}\:{be}\:\left({a}−{b}+{c}\right){x}^{\mathrm{2}}…

Question Number 210390 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $$t{\tan }^{-1}\left(\frac{1}{t}\right)=f\left(t\right)$$$$\underset{x\to \mathrm{\infty }}{\lim }f\left(x\right)=1\Rightarrow \mathrm{\exists }M\in {\mathbb{R}}_{+}\mathrm{\forall }x⩾M\frac{1}{2}⩽f\left(x\right)⩽\frac{3}{2}$$$$\Rightarrow\forall{x}\geqslant{M} \…