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Category: Algebra

a-2-b-1-1999-how-many-natural-solutions-of-the-equation-a-b-have-

Question Number 199133 by hardmath last updated on 28/Oct/23 $$\mathrm{a}^{\mathrm{2}} \mathrm{b}\:−\:\mathrm{1}\:=\:\mathrm{1999} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{natural}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{have}? \\ $$ Answered by Rasheed.Sindhi last updated on 28/Oct/23 $$\mathrm{a}^{\mathrm{2}}…

8-x-1-1-4-x-1-x-1-1-4-5-x-2-1-2-3-1-4-x-

Question Number 199159 by cortano12 last updated on 28/Oct/23 $$\:\sqrt[{\mathrm{4}}]{\mathrm{8}\left(\mathrm{x}+\mathrm{1}\right)}\:+\sqrt[{\mathrm{4}}]{\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}}\:=\sqrt[{\mathrm{4}}]{\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}}\: \\ $$$$\:\mathrm{x}=? \\ $$ Answered by Frix last updated on 28/Oct/23 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\…

a-2-b-73-b-2-a-73-find-a-b-

Question Number 199112 by hardmath last updated on 28/Oct/23 $$\begin{cases}{\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{b}\:=\:\mathrm{73}}\\{\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{a}\:=\:\mathrm{73}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{a},\mathrm{b}\:=\:? \\ $$ Answered by mr W last updated on 28/Oct/23 $$\left({i}\right)−\left({ii}\right): \\ $$$${a}^{\mathrm{2}}…

Q-are-the-roots-of-the-following-equation-find-the-value-of-Eq-n-x-3-2x-2-x-2-0-E-

Question Number 199109 by mnjuly1970 last updated on 28/Oct/23 $$ \\ $$$$\:{Q}:\:\:\:\:\alpha\:,\:\beta\:,\gamma\:{are}\:{the}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:.\:{find}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:{Eq}^{\:{n}} \::\:\:\:{x}^{\:\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:{E}\:=\:\frac{\alpha}{\beta\:+\gamma}\:+\frac{\beta}{\alpha\:+\gamma}\:+\frac{\gamma}{\alpha+\:\beta} \\ $$$$…

Let-the-polynomial-p-x-5x-3-3x-2-10-have-roots-a-b-and-c-What-is-the-value-of-a-b-c-b-c-a-c-a-b-

Question Number 199092 by necx122 last updated on 27/Oct/23 $${Let}\:{the}\:{polynomial}\:{p}\left({x}\right)=\mathrm{5}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{10} \\ $$$${have}\:{roots}\:{a},{b}\:{and}\:{c}.\:{What}\:{is}\:{the}\:{value} \\ $$$${of}\:\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}? \\ $$ Answered by Rasheed.Sindhi last updated on 28/Oct/23…

Find-the-polynomial-with-roots-that-exceed-the-roots-of-f-x-3x-3-14x-2-x-62-0-by-3-Hence-determine-the-value-of-1-a-3-1-b-3-1-c-3-where-a-b-and-c-are-roots-

Question Number 198968 by necx122 last updated on 26/Oct/23 $${Find}\:{the}\:{polynomial}\:{with}\:{roots}\:{that} \\ $$$${exceed}\:{the}\:{roots}\:{of}\: \\ $$$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{3}} −\mathrm{14}{x}^{\mathrm{2}} +{x}+\mathrm{62}=\mathrm{0}\:{by}\:\mathrm{3}.\:{Hence} \\ $$$${determine}\:{the}\:{value}\:{of}\:\frac{\mathrm{1}}{{a}+\mathrm{3}}+\frac{\mathrm{1}}{{b}+\mathrm{3}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}, \\ $$$${where}\:{a},{b}\:{and}\:{c}\:{are}\:{roots}. \\ $$ Answered by Rasheed.Sindhi…