Question Number 210467 by maths_plus last updated on 09/Aug/24 $$\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+…+\sqrt{\mathrm{n}}\:\:\:\mathrm{irrational}\:??? \\ $$ Answered by Frix last updated on 10/Aug/24 $$\mathrm{Yes}!!! \\ $$ Commented by maths_plus…
If-the-roots-of-the-quadratic-equation-a-b-c-x-2-c-b-a-x-2-b-c-0-are-real-and-equal-then-find-a-b-c-
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 $${not}\:{qudratic}\:,{it}\:{should}\:{be}\:\left({a}−{b}+{c}\right){x}^{\mathrm{2}}…
Question Number 210392 by peter frank last updated on 08/Aug/24 Commented by mr W last updated on 09/Aug/24 $${in}\:\left({b}\right)\:{it}\:{is}\:\frac{\mathrm{1}}{\mathrm{7}},\:{not}\:\frac{\mathrm{1}}{\mathrm{4}}. \\ $$ Answered by mr W…
Question Number 210390 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${t}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)={f}\left({t}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{1}\Rightarrow\exists{M}\in\mathbb{R}_{+} \:\forall{x}\geqslant{M}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant{f}\left({x}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow\forall{x}\geqslant{M} \\…
Question Number 210356 by hardmath last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210355 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${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} \\ $$$$\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…
Question Number 210432 by hardmath last updated on 08/Aug/24 $$ \\ $$How many different five-digit numbers can be written from the digits 1,2,3,4,5,6,7,8 if the…
Question Number 210375 by Spillover last updated on 08/Aug/24 Commented by som(math1967) last updated on 08/Aug/24 $$\:\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 210369 by peter frank last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210368 by peter frank last updated on 08/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com