Question Number 91599 by john santu last updated on 01/May/20 Commented by mr W last updated on 01/May/20 $${x}=\mathrm{0}\:{is}\:{a}\:{solution}. \\ $$$${since}\:\frac{{d}\left({LHS}\right)}{{dx}}>\frac{{d}\left({RHS}\right)}{{dx}}=\mathrm{4}, \\ $$$${x}=\mathrm{0}\:{is}\:{also}\:{the}\:{only}\:{one}\:{solution}. \\ $$…
Question Number 157120 by cortano last updated on 20/Oct/21 $$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}\right)=? \\ $$ Answered by puissant last updated on 20/Oct/21 $$\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}\right)=\frac{\mathrm{1}}{\mathrm{9}}\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 26053 by tawa tawa last updated on 18/Dec/17 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{9x}\:+\:\mathrm{2}\:=\:\mathrm{0}\:\:\mathrm{and}\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{kx}\:+\:\mathrm{5}\:=\:\mathrm{0}\:\:\mathrm{have}\:\mathrm{a}\:\mathrm{common}\:\mathrm{root},\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{2k}^{\mathrm{2}} \:+\:\mathrm{63k}\:−\:\mathrm{414}\:=\:\mathrm{0}\:,\:\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{k}\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{k}\:>\:\mathrm{9}.\mathrm{3} \\ $$ Answered by kaivan.ahmadi last updated on 18/Dec/17…
Question Number 26042 by sanjib bibhar last updated on 18/Dec/17 $${ax}^{\mathrm{2}} −{bx}=\mathrm{0} \\ $$ Commented by sanjib bibhar last updated on 19/Dec/17 $${thanks} \\ $$…
Question Number 91560 by ar247 last updated on 01/May/20 $${x}=\frac{\mathrm{1}+\sqrt{\mathrm{2004}}}{\mathrm{2}} \\ $$$$\mathrm{4}{x}^{\mathrm{3}} −\mathrm{2007}{x}−\mathrm{2000}=? \\ $$ Commented by Prithwish Sen 1 last updated on 01/May/20 $$\mathrm{x}^{\mathrm{3}}…
Question Number 157080 by amin96 last updated on 19/Oct/21 Commented by cortano last updated on 20/Oct/21 $$\Rightarrow\mathrm{1}+\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}=\frac{\mathrm{3sin}\:\mathrm{2}{x}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{3}−\mathrm{cos}\:\mathrm{2}{x}=\mathrm{3sin}\:\mathrm{2}{x} \\ $$$$\Rightarrow\mathrm{3}−\mathrm{cos}\:\mathrm{2}{x}=\mathrm{3}\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)} \\ $$$$\Rightarrow\mathrm{9}+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)−\mathrm{6cos}\:\left(\mathrm{2}{x}\right)=\mathrm{9}−\mathrm{9cos}\:^{\mathrm{2}}…
Question Number 157071 by MathSh last updated on 19/Oct/21 $$\mathrm{if}\:\:\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}\:\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{sin}\boldsymbol{\mathrm{x}}}\:+\:\frac{\mathrm{2}}{\pi\mathrm{x}}\:\leqslant\:\left(\mathrm{1}\:-\:\frac{\mathrm{2}}{\pi}\right)^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{2}}{\pi} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 157057 by amin96 last updated on 19/Oct/21 $$\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{13}}+\frac{\mathrm{1}}{\mathrm{19}}={a} \\ $$$${find}\:\frac{\mathrm{2}}{\mathrm{7}}+\frac{\mathrm{4}}{\mathrm{13}}+\frac{\mathrm{6}}{\mathrm{19}}=? \\ $$ Commented by aliyn last updated on 19/Oct/21 $$\frac{\mathrm{2}}{\mathrm{7}}+\frac{\mathrm{4}}{\mathrm{13}}+\frac{\mathrm{6}}{\mathrm{19}}=\left(\frac{\mathrm{2}}{\mathrm{7}}\:+\:\frac{\mathrm{2}}{\mathrm{13}}\:+\frac{\mathrm{2}}{\mathrm{19}}\:\right)+\left(\frac{\mathrm{2}}{\mathrm{13}}+\frac{\mathrm{4}}{\mathrm{19}}\right) \\ $$$$ \\…
Question Number 157053 by depressiveshrek last updated on 19/Oct/21 $$\mathrm{If}\:\mathrm{you}\:\mathrm{want}\:\mathrm{to}\:\mathrm{easily}\:\mathrm{write}\:\mathrm{any}\:\mathrm{quadratic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{vertex}\:\mathrm{form},\:\mathrm{just}\:\mathrm{use}\:\mathrm{these}\:\mathrm{formulas}: \\ $$$$\: \\ $$$${f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\: \\ $$$$\mathrm{if}\:{a}>\mathrm{0},\:\mathrm{then}: \\ $$$${f}\left({x}\right)=\left({x}+\frac{{b}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{{b}}{\mathrm{2}}\right)^{\mathrm{2}} +{c} \\ $$$$\:…
Question Number 157044 by MathSh last updated on 18/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\mathrm{sin2}\boldsymbol{\mathrm{x}}\:+\:\mathrm{4cos}^{\mathrm{2}} \boldsymbol{\mathrm{x}}\:+\:\mathrm{1}\right)\left(\mathrm{cos5}\boldsymbol{\mathrm{x}}\:-\:\mathrm{cos}\boldsymbol{\mathrm{x}}\right)<\mathrm{0} \\ $$ Answered by mindispower last updated on 19/Oct/21 $$\mathrm{1}+{sin}\left(\mathrm{2}{x}\right)=\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\mathrm{2}} \\ $$$$\Leftrightarrow\left(\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\mathrm{2}}…