Category: Algebra

Question Number 210362 by MATHEMATICSAM last updated on 10/Sep/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left({a}\:−\:{b}\:+\:{c}\right){x}^{\mathrm{2}} \:+\:\left({c}\:−\:{b}\:−\:{a}\right){x}\:+\:\mathrm{2}\left({b}\:−\:{c}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{equal}\:\mathrm{then}\:\mathrm{find}\:\frac{{a}}{{b}\:−\:{c}}\:. \\ $$ 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 $${t}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)={f}\left({t}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{1}\Rightarrow\exists{M}\in\mathbb{R}_{+} \:\forall{x}\geqslant{M}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant{f}\left({x}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow\forall{x}\geqslant{M} \\…

Question Number 210355 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\gamma{ab}\overset{{AM}−{GM}} {\leqslant}\left(\frac{\gamma}{\mathrm{2}}+\mathrm{1}\right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right);\gamma>\mathrm{0} \\ $$$$\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…

Question Number 210375 by Spillover last updated on 08/Aug/24 Commented by som(math1967) last updated on 08/Aug/24 $$\:\boldsymbol{{if}}\:\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{x}}+\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{y}}+\mathrm{sin}^{−\mathrm{1}} \boldsymbol{{z}}=\boldsymbol{\pi} \\ $$$${then}\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} +\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 210368 by peter frank last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com