Question Number 215164 by MathematicalUser2357 last updated on 30/Dec/24 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\:{x}^{\mathrm{2}} −\mathrm{12}{x}+{k}=\mathrm{0}\:\mathrm{is}\:\alpha,\:\alpha^{\mathrm{2}} , \\ $$$$\mathrm{Then}\:\mathrm{solve}\:\mathrm{for}\:\alpha\:\mathrm{and}\:{k}\:\mathrm{or}\:\mathrm{I}\:\mathrm{will}\:\mathrm{force}\:\mathrm{you}\:\mathrm{to}\:\mathrm{solve} \\ $$ Answered by A5T last updated on 30/Dec/24 $$\alpha+\alpha^{\mathrm{2}} =\mathrm{12}\Rightarrow\alpha=−\mathrm{4}\:\mathrm{or}\:\mathrm{3}…
Question Number 215167 by MathematicalUser2357 last updated on 30/Dec/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\:{x}^{\mathrm{2}} −\mathrm{2}{x}−{m}+\mathrm{1}=\mathrm{0}\:\mathrm{has}\:\mathrm{two}\:\mathrm{different}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{roots}\:\alpha,\:\beta, \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{m}\:\left(\mathrm{For}\:\mathrm{example},\:\mathrm{0}<{m}<\mathrm{3}\right)\:\mathrm{or}\:\mathrm{I}\:\mathrm{will}\:\mathrm{force}\:\mathrm{you}\:\mathrm{to}\:\mathrm{determine} \\ $$ Answered by A5T last updated on 30/Dec/24 $$\mathrm{x}_{\mathrm{1},\mathrm{2}} =\frac{\mathrm{2}\underset{−} {+}\sqrt{\mathrm{4}−\mathrm{4}\left(\mathrm{1}−\mathrm{m}\right)}}{\mathrm{2}}=\mathrm{1}\underset{−}…
Question Number 215177 by Ismoiljon_008 last updated on 30/Dec/24 $$ \\ $$$$\:\:\:{x}^{\mathrm{3}} \:+\:{x}^{\mathrm{2}} \:+\:{x}\:=\:−\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\mathcal{F}{ind}\:{the}\:{value}\:{of}\:\:{x}\:\:!\: \\ $$$$ \\ $$$$\:\:\:\mathcal{H}{elp}\:{me},\:\:{please} \\ $$$$ \\ $$ Answered…
Question Number 215168 by MathematicalUser2357 last updated on 30/Dec/24 $$\mathrm{Let}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} +\mathrm{2}{mx}+{m}^{\mathrm{2}} −\mathrm{2}{m}+\mathrm{3}=\mathrm{0}\:\mathrm{is}\:\alpha,\:\beta\left(\mathrm{For}\:\alpha<\beta\right), \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Find}\:\left(\alpha−\beta\right)^{\mathrm{2}} \:\mathrm{Using}\:{m}. \\ $$$$\left(\mathrm{3}\right)\:\mathrm{If}\:\beta−\alpha=\mathrm{2},\:\mathrm{Solve}\:\mathrm{for}\:{m}. \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{solve}\:\mathrm{it},\:\mathrm{I}\:\mathrm{will}\:\mathrm{force}\:\mathrm{you}\:\mathrm{to}\:\mathrm{solve}. \\ $$ Answered by A5T last…
Question Number 215114 by issac last updated on 29/Dec/24 Answered by TonyCWX08 last updated on 29/Dec/24 $$\oint={Integral}\:{over}\:{a}\:{closed}\:{path} \\ $$$$\subset\int\int\supset={Integral}\:{over}\:{a}\:{closed}\:{surface} \\ $$$$\subset\int\int\int\supset={Integral}\:{over}\:{a}\:{closed}\:{region}\:{in}\:\mathrm{3}{D}\:{space}. \\ $$ Answered by…
Question Number 215086 by mahdijebraili last updated on 28/Dec/24 Answered by MathematicalUser2357 last updated on 28/Dec/24 $$\mathrm{Here}'\mathrm{s}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{as}\:\mathrm{a}\:\mathrm{drawing}: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 215107 by arkanmathematics63 last updated on 28/Dec/24 Commented by arkanmathematics63 last updated on 28/Dec/24 $${C}\:{is}\:{the}\:{combination} \\ $$ Commented by mr W last updated…
Question Number 215048 by Hanuda354 last updated on 27/Dec/24 $$\mathrm{Solve}\:\:\mathrm{for}\:\:{a},\:{b},\:{c}\:\in\:\mathbb{R} \\ $$$$\:\:\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}+{c}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}+{a}}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{a}+{b}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented by Abdullahrussell last updated on 27/Dec/24…
Question Number 215033 by MrGaster last updated on 27/Dec/24 $$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{\mathrm{sin}\theta−\mathrm{cos}\varphi−\mathrm{sin}\theta\mathrm{cos}\varphi}{\left(\mathrm{2sin}\theta−\mathrm{2cos}\varphi−\mathrm{2sin}\theta\mathrm{cos}\varphi+\mathrm{3}\right)^{\mathrm{3}/\mathrm{2}} }{d}\theta{d}\varphi \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 214997 by MrGaster last updated on 25/Dec/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=−\infty} {\overset{+\infty} {\sum}}\frac{{k}^{\mathrm{2}} +{k}+\mathrm{1}}{{k}^{\mathrm{4}} +\mathrm{1}}=? \\ $$$$ \\ $$ Answered by mr W last…