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Question Number 174755 by mnjuly1970 last updated on 10/Aug/22 Commented by kaivan.ahmadi last updated on 11/Aug/22 $${I}\subseteq\sqrt{{I}},{J}\subseteq\sqrt{{J}}\Rightarrow{I}+{J}\subseteq\sqrt{{I}}+\sqrt{{J}} \\ $$$$\Rightarrow\sqrt{{I}+{J}}\subseteq\sqrt{\sqrt{{I}}+\sqrt{{J}}} \\ $$$${on}\:{the}\:{other}\:{hand} \\ $$$$\sqrt{{I}}+\sqrt{{J}}\subseteq\sqrt{{I}+{J}}\Rightarrow\sqrt{\sqrt{{I}}+\sqrt{{J}}}\subseteq \\ $$$$\sqrt{\sqrt{{I}+{J}}}=\sqrt{{I}+{J}}…
Question Number 43665 by peter frank last updated on 13/Sep/18 $$\left.\mathrm{1}\right)\:{if}\:\:{s}_{{n}\:\:} \:=\alpha^{{n}} +\beta^{{n}} +\lambda^{{n}\:} \:{where}\:\alpha,\beta,\lambda \\ $$$${are}\:{the}\:{root}\:{of}\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\:{then}\:\:{show}\:{that}\:{s}_{\mathrm{4}\:} =\frac{\mathrm{4}{abd}+\mathrm{4}{b}^{\mathrm{2}} {c}−\mathrm{2}{c}}{{a}^{\mathrm{3}} } \\…
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Question Number 174732 by oustmuchiya@gmail.com last updated on 09/Aug/22 Answered by aleks041103 last updated on 10/Aug/22 $${its}\:{not}\:{possible}\:{to}\:“{convert}''\:{a}\:{matrix} \\ $$$${into}\:{an}\:{identity}\:{matrix}. \\ $$$${what}\:{would}\:{that}\:{even}\:{mean}? \\ $$ Terms of…
Question Number 109193 by mr W last updated on 21/Aug/20 $${solve}\: \\ $$$${x}^{{x}^{\mathrm{3}} } =\mathrm{5} \\ $$ Commented by aurpeyz last updated on 21/Aug/20 $$\:{x}^{{x}^{\mathrm{3}}…
Question Number 174719 by AgniMath last updated on 09/Aug/22 Answered by behi834171 last updated on 09/Aug/22 $$\boldsymbol{{a}}+\boldsymbol{{b}}\neq\mathrm{0} \\ $$$$\Rightarrow\frac{\boldsymbol{{a}}+\boldsymbol{{b}}}{\boldsymbol{{ab}}}=\frac{\mathrm{1}}{\boldsymbol{{a}}+\boldsymbol{{b}}}\Rightarrow\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)^{\mathrm{2}} =\boldsymbol{{ab}}\Rightarrow \\ $$$$\Rightarrow\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{ab}}+\boldsymbol{{b}}^{\mathrm{2}} =\mathrm{0}\overset{\boldsymbol{{a}}\neq\boldsymbol{{b}}} {\Rightarrow}\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{a}}^{\mathrm{2}}…
Question Number 174709 by AgniMath last updated on 09/Aug/22 Commented by MJS_new last updated on 09/Aug/22 $$\pm\mathrm{1}? \\ $$ Commented by infinityaction last updated on…
Question Number 109160 by john santu last updated on 21/Aug/20 $${Find}\:{the}\:{equation}\:{of}\:{line}\:{through} \\ $$$${the}\:{point}\:{of}\:{intersection}\:{of}\:{the} \\ $$$${line}\:{x}+\mathrm{3}{y}−\mathrm{11}=\mathrm{0}\:{and}\:\mathrm{5}{x}−\mathrm{4}{y}+\mathrm{2}=\mathrm{0} \\ $$$${and}\:{perpendicular}\:{to}\:\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{9}=\mathrm{0}. \\ $$ Answered by bemath last updated on…
Question Number 174684 by mnjuly1970 last updated on 08/Aug/22 $$ \\ $$$$\boldsymbol{\mathrm{Q}}:\:\:\boldsymbol{\mathrm{I}}\:,\:\boldsymbol{\mathrm{J}}\:\:\boldsymbol{{are}}\:\boldsymbol{{two}}\:\boldsymbol{{ideals}}\:\boldsymbol{{of}}\:\:\boldsymbol{{commutative}}\: \\ $$$$\:\:\:\:\boldsymbol{{ring}}\:,\:\left(\:\boldsymbol{\mathrm{R}}\:,\oplus,\: \:\right)\:.\boldsymbol{{prove}}\:\boldsymbol{{that}}\:: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\sqrt{\:\boldsymbol{\mathrm{I}}\:\cap\:\boldsymbol{\mathrm{J}}\:}\:\:\overset{?} {=}\:\sqrt{\:\boldsymbol{\mathrm{I}}\:}\:\:\cap\:\:\sqrt{\:\boldsymbol{\mathrm{J}}\:}\:\:\:\:\:\boldsymbol{{m}}.\boldsymbol{{n}} \\ $$$$\:\:\:\:\boldsymbol{{note}}\::\:\sqrt{\boldsymbol{\mathrm{I}}\:}\:=\:\left\{\:\boldsymbol{{x}}\:\in\:\boldsymbol{\mathrm{R}}\:\mid\:\exists\:\boldsymbol{{n}}\in\:\mathbb{N}\:,\:\boldsymbol{{x}}^{\:\boldsymbol{{n}}} \:\in\:\boldsymbol{\mathrm{I}}\:\right\}\: \\ $$$$\:…