Question Number 152663 by mr W last updated on 31/Aug/21 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} -\mathrm{x}+\mathrm{3}=\mathrm{0}\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}. \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{monic}\:\mathrm{polynomial}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\:\mathrm{a}^{\mathrm{5}} ,\:\mathrm{b}^{\mathrm{5}} \:\mathrm{and}\:\:\mathrm{c}^{\mathrm{5}} . \\ $$$$\left[{Q}\mathrm{152396}\right] \\ $$ Answered by…
Question Number 21578 by ANTARES_VY last updated on 28/Sep/17 $$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{whole}}\:\:\boldsymbol{\mathrm{part}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{A}}? \\ $$$$\boldsymbol{\mathrm{A}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+……+\frac{\mathrm{1}}{\:\sqrt{\mathrm{9999}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{10000}}}. \\ $$ Commented by Tinkutara last updated on 28/Sep/17 $$\mathrm{Almost}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{KVS}\:\mathrm{JMO}\:\mathrm{2016}. \\ $$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{available}\:\mathrm{on}\:\mathrm{net}. \\…
Question Number 152625 by Dandelion last updated on 30/Aug/21 $${x}^{\mathrm{4}} +{c}_{\mathrm{3}} {x}^{\mathrm{3}} +{c}_{\mathrm{2}} {x}^{\mathrm{2}} +{c}_{\mathrm{1}} {x}+{c}_{\mathrm{0}} =\mathrm{0} \\ $$$$\mathrm{for}\:{c}_{{n}} \in\mathbb{R}\:\mathrm{this}\:\mathrm{can}\:\mathrm{have} \\ $$$$\mathrm{4}\:\mathrm{unique}\:\mathrm{zeros}\:\in\mathbb{R} \\ $$$$\mathrm{2}\:\mathrm{unique}\:\mathrm{zeros}\:+\:\mathrm{1}\:\mathrm{double}\:\mathrm{zero}\:\in\mathbb{R} \\…
Question Number 87093 by M±th+et£s last updated on 02/Apr/20 $$\lfloor\frac{{x}−\mathrm{1}}{\mathrm{4}}\rfloor+\lfloor\frac{{x}−\mathrm{2}}{\mathrm{3}}\rfloor=\lfloor\frac{{x}−\mathrm{3}}{\mathrm{2}}\rfloor \\ $$ Commented by M±th+et£s last updated on 02/Apr/20 $${slove}\:{the}\:{equation} \\ $$ Commented by MJS…
Question Number 152626 by mathdanisur last updated on 30/Aug/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}-\mathrm{1}}\:+\:\frac{\mathrm{2}}{\mathrm{x}-\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{x}-\mathrm{3}}\:+\:\frac{\mathrm{4}}{\mathrm{x}-\mathrm{4}}\:=\:\mathrm{2x}^{\mathrm{2}} -\mathrm{5x}-\mathrm{4} \\ $$ Answered by MJS_new last updated on 30/Aug/21 $${x}=\mathrm{0} \\ $$$${x}=\frac{\mathrm{5}}{\mathrm{2}}…
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Question Number 21531 by Princejak last updated on 26/Sep/17 $${Factorise}\:{the}\:{equation}\:{by}\:{factor}\:{theorem} \\ $$$$\mathrm{12}\hat {{x}}\mathrm{3}\:+\:\mathrm{4}\hat {{x}}\mathrm{2}−\mathrm{3}{x}−\mathrm{1} \\ $$ Commented by Princejak last updated on 26/Sep/17 $${please}\:{answer} \\…
Question Number 21526 by tawa tawa last updated on 26/Sep/17 Commented by tawa tawa last updated on 26/Sep/17 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}.\:\mathrm{Thanks}\:\mathrm{in}\:\mathrm{advance}. \\ $$ Commented by $@ty@m last…
Question Number 152596 by liberty last updated on 30/Aug/21 Answered by som(math1967) last updated on 30/Aug/21 $$\boldsymbol{{let}}\:\frac{\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}}{\mathrm{4}\boldsymbol{{y}}+\mathrm{3}}=\frac{\mathrm{4}\boldsymbol{{y}}+\mathrm{1}}{\mathrm{9}}=\frac{\mathrm{11}}{\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}}=\boldsymbol{{k}} \\ $$$$\left[\because\boldsymbol{{a}}=\boldsymbol{{b}}=\boldsymbol{{c}}\right] \\ $$$$\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}=\boldsymbol{{k}}\left(\mathrm{4}\boldsymbol{{y}}+\mathrm{3}\right) \\ $$$$\mathrm{4}\boldsymbol{{y}}+\mathrm{1}=\mathrm{9}\boldsymbol{{k}} \\ $$$$\mathrm{11}=\boldsymbol{{k}}\left(\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}\right)…
Question Number 87050 by jagoll last updated on 02/Apr/20 $$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+\mathrm{1}}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{x}+\mathrm{y}\:+\:\mathrm{xy}\:=\:\mathrm{5}\:? \\ $$ Commented by john santu last updated on 02/Apr/20 $$\Rightarrow{x}+{y}+{xy}+\mathrm{1}\:=\:\mathrm{6}\:\Rightarrow{x}\left({y}+\mathrm{1}\right)=\mathrm{5}−{y}…