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Category: Algebra

Let-p-and-q-are-the-roots-of-x-2-2mx-5n-0-and-m-and-n-are-the-roots-of-x-2-2px-5q-0-If-p-q-m-n-then-the-value-of-p-q-m-n-is-

Question Number 31320 by Joel578 last updated on 06/Mar/18 $$\mathrm{Let}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{2}{mx}\:−\:\mathrm{5}{n}\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:{m}\:\mathrm{and}\:{n}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{2}{px}\:−\:\mathrm{5}{q}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{p}\:\neq\:{q}\:\neq\:{m}\:\neq\:{n},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:+\:{q}\:+\:{m}\:+\:{n}\:\mathrm{is}\:… \\ $$ Answered…

Question-162382

Question Number 162382 by HongKing last updated on 29/Dec/21 Answered by Rasheed.Sindhi last updated on 29/Dec/21 $$\underset{−} {\left.\begin{matrix}{\:\:\:\:\:\:\:\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\right)\left(\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{1}}\:\right)=\mathrm{2011}}\\{\:\:\:\:\:\:\:\:\:\mathrm{x}+\mathrm{y}=\frac{\mathrm{2010}}{\:\sqrt{\mathrm{2011}}}\:\:}\end{matrix}\right\}\:\:\:\:\:\:\:\:\:\:}\:\: \\ $$$$\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\right)\centerdot\frac{\left(\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{1}}\:\right)\left(\mathrm{y}−\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{1}}\:\right)}{\left(\mathrm{y}−\sqrt{\mathrm{y}^{\mathrm{2}}…

Let-x-1-x-2-x-3-be-the-roots-of-the-equation-x-3-3x-5-0-Then-the-value-of-expression-x-1-1-x-1-x-2-1-x-2-x-3-1-x-3-is-equal-to-

Question Number 162367 by cortano last updated on 29/Dec/21 $$\:\:{Let}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} \:{be}\:{the}\:{roots}\:{of}\:{the}\: \\ $$$${equation}\:{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{5}=\mathrm{0}\:.\:{Then}\:{the} \\ $$$${value}\:{of}\:{expression}\:\left({x}_{\mathrm{1}} +\frac{\mathrm{1}}{{x}_{\mathrm{1}} }\right)\left({x}_{\mathrm{2}} +\frac{\mathrm{1}}{{x}_{\mathrm{2}} }\right)\left({x}_{\mathrm{3}} +\frac{\mathrm{1}}{{x}_{\mathrm{3}} }\right)\:{is} \\…

If-2f-x-f-1-x-x-2-determine-f-x-

Question Number 96829 by bobhans last updated on 05/Jun/20 $$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$ Commented by john santu last updated on 05/Jun/20 $$\mathrm{replace}\:\mathrm{x}\:\mathrm{by}\:\mathrm{1}−\mathrm{x}\:\mathrm{into}\:\mathrm{eq}\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2f}\left(\mathrm{1}−\mathrm{x}\right)\:+\mathrm{f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \\…

Find-all-set-of-ordered-triple-s-x-y-z-x-y-z-such-that-x-y-1-z-3-x-2-y-2-5-1-z-2-7-x-3-y-3-19-1-z-3-Please-show-your-solution-

Question Number 31286 by 6123 last updated on 05/Mar/18 $${Find}\:{all}\:{set}\:{of}\:{ordered}\:{triple}/{s}\:\left({x},{y},{z}\right),\:\:{x},{y},{z}\in\Re,\:{such}\:{that} \\ $$$${x}−{y}=\mathrm{1}−{z} \\ $$$$\mathrm{3}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{5}\left(\mathrm{1}−{z}^{\mathrm{2}} \right) \\ $$$$\mathrm{7}\left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)=\mathrm{19}\left(\mathrm{1}−{z}^{\mathrm{3}} \right). \\ $$$${Please}\:{show}\:{your}\:{solution}. \\…

u-2-v-v-2-u-12-1-u-1-v-1-3-find-u-and-v-

Question Number 96821 by bobhans last updated on 05/Jun/20 $$\begin{cases}{\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{v}}\:+\:\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{u}}\:=\:\mathrm{12}}\\{\frac{\mathrm{1}}{\mathrm{u}}\:+\:\frac{\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases}\:.\:\mathrm{find}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:? \\ $$ Answered by john santu last updated on 05/Jun/20 Commented by bobhans…

d-2-y-dx-2-3-dy-dx-4y-tan-x-log-cos-x-

Question Number 162338 by HongKing last updated on 28/Dec/21 $$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:-\:\mathrm{3}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)\:-\:\mathrm{4y}\:=\:\mathrm{tan}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{cos}\left(\mathrm{x}\right)\right) \\ $$ Answered by Ar Brandon last updated on 29/Dec/21 $$\mathrm{y}''−\mathrm{3y}'−\mathrm{4y}=\mathrm{tan}{x}\centerdot\mathrm{ln}\left(\mathrm{cos}{x}\right) \\ $$$$\mathrm{For}\:\mathrm{y}_{\mathrm{gh}}…