Question Number 154552 by 0731619 last updated on 19/Sep/21
Commented by Rasheed.Sindhi last updated on 20/Sep/21
$$\bullet\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{compitition}\:\mathrm{to}\:\mathrm{make} \\ $$$$\boldsymbol{\mathrm{posts}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{others}}\:'\mathrm{red}-\mathrm{flaged}'\:? \\ $$$$\heartsuit\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{compitition}\:\mathrm{of}\:'\mathrm{likes}' \\ $$$$\:\:\:\mathrm{of}\:\mathrm{somebodies}\:\mathrm{to}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{own}}\:\boldsymbol{\mathrm{posts}}? \\ $$$$\blacklozenge\:\mathrm{Is}\:\mathrm{this}\:\mathrm{a}\:\boldsymbol{\mathrm{market}}\:\boldsymbol{\mathrm{place}}? \\ $$$$\boldsymbol{\mathrm{AND}}\: \\ $$$$\:\:\mathrm{winners}\:\mathrm{are}\:\mathrm{those}\:\mathrm{who}\:\mathrm{have}\:\mathrm{more} \\ $$$$\:\:\mathrm{ID}'\mathrm{s}\:\mathrm{or}\:\mathrm{more}\:\mathrm{divices}! \\ $$
Commented by Rasheed.Sindhi last updated on 19/Sep/21
$$@{mathdanisur} \\ $$$$\mathcal{H}{ow}\:{did}\:{you}\:{guess}\:{that}? \\ $$
Commented by Tinku Tara last updated on 20/Sep/21
$$\mathrm{Answering}\:\mathrm{own}\:\mathrm{question}\:\mathrm{is}\:\mathrm{very}\:\mathrm{much} \\ $$$$\mathrm{acceptable}.\:\mathrm{Almost}\:\mathrm{all}\:\mathrm{senior}\:\mathrm{mebers}\: \\ $$$$\mathrm{of}\:\mathrm{forum}\:\mathrm{post}\:\mathrm{a}\:\mathrm{quesion}\:\mathrm{which}\:\mathrm{they} \\ $$$$\mathrm{find}\:\mathrm{interesting}\:\mathrm{and}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{2}/\mathrm{3} \\ $$$$\mathrm{days}. \\ $$$$\mathrm{Posting}\:\mathrm{very}\:\mathrm{simple}\:\mathrm{question}\:\mathrm{just} \\ $$$$\mathrm{increase}\:\mathrm{noise}\:\mathrm{and}\:\mathrm{good}\:\mathrm{challenging} \\ $$$$\mathrm{questions}\:\mathrm{end}\:\mathrm{up}\:\mathrm{getting}\:\mathrm{ignored}\:\mathrm{which} \\ $$$$\mathrm{could}\:\mathrm{create}\:\mathrm{good}\:\mathrm{discussion}\:\mathrm{on}\:\mathrm{solution} \\ $$$$\mathrm{approaches}\:\mathrm{as}\:\mathrm{well}. \\ $$
Commented by liberty last updated on 19/Sep/21
Commented by liberty last updated on 19/Sep/21
What are you saying ?
Commented by iloveisrael last updated on 20/Sep/21
Sieht aus als wärst du verrückt
Commented by mathdanisur last updated on 20/Sep/21
$$\mathrm{and}\:\:\boldsymbol{\mathrm{i}}\mathrm{loveisrae}\boldsymbol{\mathrm{l}}\:\:\mathrm{as}\:\mathrm{well}\:\mathrm{as}\:\mathrm{that}\:\mathrm{person} \\ $$
Commented by iloveisrael last updated on 20/Sep/21
In my opinion, let it be. do we feel harmed by that? what's the downside? We don't need to interfere in all our people's affairs. if it doesn't hurt us
Commented by Rasheed.Sindhi last updated on 20/Sep/21
$$\mathrm{Then}\:\mathrm{it}\:\mathrm{will}\:\mathrm{be}\:\mathrm{difficult}\: \\ $$$$\mathrm{for}\:\mathrm{administator}\:\mathrm{to}\:\mathrm{distinguish} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{between}\: \\ $$$$“{really}\:\boldsymbol{{able}}\:{to}\:{be}\:{red}\:{marked}'' \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\: \\ $$$$“{marked}\:{red}\:{as}\:{a}\:\boldsymbol{{revenge}}'' \\ $$
Commented by mr W last updated on 20/Sep/21
$${forum}\:{is}\:{a}\:{public}\:{for}\:{exchanging} \\ $$$${questions}\:\&\:{answers}\:{in}\:{mathematics}. \\ $$$${if}\:{somebody}\:{constantly}\:{posts}\:{pictures} \\ $$$${or}\:{other}\:{things}\:{which}\:{have}\:{nothing} \\ $$$${to}\:{do}\:{with}\:{exchanging}\:{mathematics}, \\ $$$${i}\:{don}'{t}\:{feel}\:{hurt},\:{but}\:{disturbed}. \\ $$
Commented by mathdanisur last updated on 20/Sep/21
$$\boldsymbol{\mathrm{S}}\mathrm{er},\:\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{or}\:\mathrm{more}\:\mathrm{profiles}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{person}\:\mathrm{and}\:\mathrm{l}\:\mathrm{mentioned}\:\mathrm{it},\:\mathrm{he}\:\mathrm{knowes} \\ $$$$\mathrm{who}\:\mathrm{he}\:\mathrm{and}\:\mathrm{that}\:\mathrm{person}\:\mathrm{paints}\:\mathrm{what} \\ $$$$\mathrm{l}\:\mathrm{share}\:\mathrm{in}\:\mathrm{red},\:\mathrm{do}\:\mathrm{his}\:\mathrm{best},\:\mathrm{nothing}\:\mathrm{will} \\ $$$$\mathrm{chang}! \\ $$
Commented by liberty last updated on 20/Sep/21
try to explain if someone posted a question and then someone answered whether it was the same person, what were your losses and what bothered you.
Commented by mr W last updated on 20/Sep/21
$${if}\:{someone}\:{don}'{t}\:{want}\:{to}\:{exchange}\: \\ $$$${with}\:{others},\:{he}\:{doesn}'{t}\:{need}\:{to}\:{use} \\ $$$${the}\:{forum}\:{function}.\:{people}\:{who}\:{use} \\ $$$${different}\:{identities}\:{to}\:{play}\:{the}\:{roles} \\ $$$${of}\:{questioner}\:{and}\:{answerer}\:{as}\:{well} \\ $$$${are}\:{cheating}\:{themselves}.\:\:{i}\:{don}'{t} \\ $$$${have}\:{any}\:{loss}\:{when}\:{other}\:{people}\: \\ $$$${cheat}\:{themselves},\:{i}\:{just}\:{think}\:{it}'{s} \\ $$$${non}−{sense}.\:{or}\:{you}\:{don}'{t}\:{think}\:{so}? \\ $$
Commented by mathdanisur last updated on 20/Sep/21
$$\boldsymbol{\mathrm{S}}\mathrm{er},\:\mathrm{yes}\:\mathrm{you}\:\mathrm{are}\:\mathrm{right},\:\mathrm{thanks}. \\ $$
Commented by liberty last updated on 20/Sep/21
Mr. W, I noticed that you are the one who very often interferes in people's affairs, you position yourself as a traffic policeman who always determines whether people are right or wrong. those of you who always feel disturbed by posts like mister zainal. you are very great . 5 stars for you.
Commented by liberty last updated on 20/Sep/21
in this forum every member is free to post as long as what is posted does not offend or hurt us. let it be. After all, if you don't want to read it, don't read it. simple isn't it?
Commented by liberty last updated on 20/Sep/21
it's not a matter of reasonable or unreasonable. Don't make your measurements to measure others. the size we use for us personally. good for us is not necessarily good for others.
Commented by mr W last updated on 20/Sep/21
$${i}\:{don}'{t}\:{judge}\:{whether}\:{people}\:{are}\:{right} \\ $$$${or}\:{wrong}.\:{i}\:{raraly}\:{red}\:{flag}\:{other} \\ $$$${people}'{s}\:{posts}.\:{but}\:{when}\:{i}\:{see}\:{that} \\ $$$${some}\:{people}\:{post}\:{things}\:{which}\:{are} \\ $$$${not}\:{the}\:{original}\:{purpose}\:{of}\:{the}\:{forum}, \\ $$$${i}\:{just}\:{tell}\:{them}\:{my}\:{opinion}.\:{since}\:{the}\: \\ $$$${forum}\:{has}\:{no}\:{real}\:{administrator} \\ $$$${in}\:{duty},\:{it}\:{depents}\:{on}\:{us}\:{all}\:{if}\:{the} \\ $$$${forum}\:{can}\:{remain}\:{clear}.\:{i}\:{personally} \\ $$$${have}\:{nothing}\:{against}\:{anybody}\:{in}\:{the} \\ $$$${forum}. \\ $$
Commented by mr W last updated on 20/Sep/21
$${if}\:{you}\:{let}\:{people}\:{do}\:{what}\:{has}\:{nothing} \\ $$$${to}\:{do}\:{with}\:{the}\:{forum},\:{the}\:{forum}\:{will} \\ $$$${become}\:{a}\:{place}\:{full}\:{of}\:{carbage}.\:{do} \\ $$$${you}\:{want}\:{it}\:{be}\:{such}\:{a}\:{place}? \\ $$
Commented by liberty last updated on 20/Sep/21
Dear Mr. W, again I say if there are members who post questions and no one answers then those who post provide answers, leave it alone, I'm sure someone will benefit from that answer. on the forum there are many statuses whether it's student, student or teacher or lecturer. Again I say don't make your size to measure others. problem member using 2 ID leave it alone. Don't get distracted with other people's business. if you are nosy it just shows you are arrogant in this forum. 5 stars for you
Commented by talminator2856791 last updated on 20/Sep/21
$$\:\mathrm{it}\:\mathrm{is}\:\mathrm{also}\:\mathrm{annoying}\:\mathrm{that}\:\mathrm{someone}\: \\ $$$$\:\mathrm{answers}\:\mathrm{their}\:\mathrm{own}\:\mathrm{questions}. \\ $$
Commented by liberty last updated on 20/Sep/21
$${that}'{s}\:{his}\:{problem}\:,\:{want}\:{to} \\ $$$${post}\:{a}\:{question}\:{and}\:{he}\:{answers} \\ $$$${himself}\:{let}\:{it}\:{be}\:{the}\:{problem}. \\ $$$${if}\:{you}\:{feel}\:{annoying}\:{just}\:{keep} \\ $$$${it}\:{in}\:{your}\:{heart}\:{that}\:{resentful} \\ $$$${feeling}.\:{that}'{s}\:{your}\:{problem}. \\ $$
Commented by mr W last updated on 20/Sep/21
$${liberty}\:{sir}:\:{i}\:{decided}\:{not}\:{to}\:{discuss} \\ $$$${with}\:{you}\:{further}\:{about}\:{this}\:{matter}. \\ $$$${actually}\:{you}\:{didn}'{t}\:{understand}\:{and} \\ $$$${din}'{t}\:{really}\:{look}\:{at}\:{what}\:{i}\:{did}.\:{i}\:{never} \\ $$$${requested}\:{people}\:{to}\:{do}\:{things}\:{in}\:{the} \\ $$$${way}\:{i}\:{like}.\:{i}\:{never}\:{deleted}\:{other} \\ $$$${people}'{s}\:{posts}\:{because}\:{i}\:{don}'{t}\:{have} \\ $$$${the}\:{power}\:{to}\:{do}\:{that}\:{even}\:{i}\:{want}! \\ $$$${i}\:{even}\:{never}\:{thought}\:{that}\:{one}\:{may}\: \\ $$$${not}\:{answer}\:{his}\:{own}\:{questions}. \\ $$$${what}\:{i}\:{did}\:{is},\:{when}\:{i}\:{see}\:{that}\:{somebody} \\ $$$${doesn}'{t}\:{use}\:{the}\:{forum}\:{properly}\:{i}\:{try} \\ $$$${to}\:{explain}\:{him}\:{what}\:{i}\:{think}\:{the} \\ $$$${forum}\:{is}\:{for}.\:{sometimes}\:{i}\:{try}\:{to}\:{give} \\ $$$${him}\:{concrete}\:{hints}.\:{all}\:{what}\:{i}\:{want} \\ $$$${is}\:{that}\:{the}\:{forum}\:{is}\:{a}\:{clean}\:{place}\: \\ $$$${where}\:{we}\:{like}\:{to}\:{be}\:{to}\:{exchange}\:{our} \\ $$$${love}\:{to}\:{mathematics}.\:{certainly}\:{you} \\ $$$${have}\:{the}\:{right}\:{to}\:{say}\:{that}\:{you}\:{don}'{t} \\ $$$${care}\:{about}\:{some}\:{posts}\:{which}\:{some} \\ $$$${other}\:{people}\:{don}'{t}\:{like}.\:{but}\:{you} \\ $$$${should}\:{also}\:{accept}\:{that}\:{these}\:{other} \\ $$$${people}\:{have}\:{the}\:{right}\:{not}\:{to}\:{like}\:{those} \\ $$$${posts}.\: \\ $$$${just}\:{image}\:{we}\:{have}\:{ten}\:{such}\:{persons} \\ $$$${like}\:{that}\:{guy}\:{who}\:{constantly}\:{posts}\: \\ $$$${his}\:{own}\:{home}\:{works}\:{in}\:{the}\:{forum}\: \\ $$$${and}\:{ignores}\:{all}\:{kinds}\:{of}\:{communication} \\ $$$${other}\:{people}\:{try}\:{with}\:{him}.\:{i}\:{think} \\ $$$${after}\:{a}\:{few}\:{days}\:{the}\:{forum}\:{will} \\ $$$${become}\:{a}\:{place}\:{full}\:{of}\:{carbage}.\:{i} \\ $$$${don}'{t}\:{want}\:{this}\:{happen},\:{therefore} \\ $$$${i}\:{act}. \\ $$$${it}'{s}\:{your}\:{good}\:{right}\:{to}\:{say}\:{that}\:{i}\:{were} \\ $$$${arrogant}.\:{but}\:{i}\:{think}\:{the}\:{most}\:{people}\: \\ $$$${here}\:{may}\:{judge}\:{by}\:{themselve}\:{who}\:{is} \\ $$$${really}\:{arrogant}. \\ $$
Commented by SLVR last updated on 26/Sep/21
$$ \\ $$$${Mr}..{W}…{sir}…{afe}\overset{} {{w}} \\ $$$${people}\:{cannot} \\ $$$${understand}\:{you}\:+{vely}.. \\ $$$${but}\:{i}\:{like}\:{that}\:{sacredness} \\ $$$${thanks}…{to}\:{your}\:{services}… \\ $$$${dear}\:{professor} \\ $$
Commented by mr W last updated on 26/Sep/21
$${thanks}\:{for}\:{understanding}\:{sir}! \\ $$
Commented by Rasheed.Sindhi last updated on 26/Sep/21
$$\mathcal{S}{ir}\:{we}\:{know}\:{that}\:{you}\:{are}\:{not}\:{only} \\ $$$${an}\:\boldsymbol{{expert}}\:\boldsymbol{{mathematician}}\:{but} \\ $$$${also}\:\boldsymbol{{very}}\:\boldsymbol{{sincere}}\:{to}\:{the}\:\boldsymbol{{forum}} \\ $$$${and}\:\boldsymbol{{its}}\:\boldsymbol{{members}}. \\ $$
Commented by mr W last updated on 26/Sep/21
$${thanks}\:{sir}! \\ $$$${the}\:{same}\:{to}\:{you}! \\ $$
Commented by Rasheed.Sindhi last updated on 28/Sep/21
️
Answered by MJS_new last updated on 19/Sep/21
$$\mathrm{squaring}\:\mathrm{and}\:\mathrm{transforming} \\ $$$${x}^{\mathrm{10}} +{x}^{\mathrm{8}} −\mathrm{2}{x}^{\mathrm{6}} −\mathrm{2}{x}^{\mathrm{4}} +\mathrm{1}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{6}} −{x}^{\mathrm{2}} −\mathrm{1}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} =−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}\:\vee{x}^{\mathrm{2}} =\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{2}}−\frac{\sqrt{\mathrm{69}}}{\mathrm{18}}}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{69}}}{\mathrm{18}}} \\ $$$$\mathrm{testing}\:\mathrm{all}\:\mathrm{solution}\:\mathrm{I}\:\mathrm{get}\:\mathrm{for}\:{x}\in\mathbb{R} \\ $$$${x}=−\sqrt{−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}}\vee{x}=\sqrt{\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{2}}−\frac{\sqrt{\mathrm{69}}}{\mathrm{18}}}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{69}}}{\mathrm{18}}}} \\ $$
Answered by liberty last updated on 19/Sep/21
$$\:{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}}\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\:{let}\:{x}=\mathrm{tan}\:\theta\: \\ $$$$\Rightarrow\mathrm{tan}\:^{\mathrm{3}} \theta−\mathrm{cot}\:\theta=\frac{\mathrm{1}}{\mathrm{sec}\:\theta} \\ $$$$\Rightarrow\mathrm{tan}\:^{\mathrm{3}} \theta−\mathrm{cot}\:\theta=\mathrm{cos}\:\theta \\ $$$$\Rightarrow\frac{\mathrm{sin}\:^{\mathrm{3}} \theta}{\mathrm{cos}\:^{\mathrm{3}} \theta}−\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta}=\mathrm{cos}\:\theta \\ $$$$\Rightarrow\mathrm{sin}\:^{\mathrm{4}} \theta−\mathrm{cos}\:^{\mathrm{4}} \theta=\mathrm{cos}\:^{\mathrm{4}} \theta\:\mathrm{sin}\:\theta \\ $$$$\Rightarrow\mathrm{2cos}\:^{\mathrm{2}} \theta−\mathrm{1}=\mathrm{cos}^{\mathrm{4}} \theta\:\mathrm{sin}\:\theta \\ $$$$\Rightarrow\mathrm{2cos}\:^{\mathrm{2}} \theta−\mathrm{1}=\mathrm{cos}\:^{\mathrm{4}} \theta\:\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \theta}\: \\ $$$$\Rightarrow\mathrm{2}{q}−\mathrm{1}={q}^{\mathrm{2}} \:\sqrt{\mathrm{1}−{q}\:}\:,\:{q}=\mathrm{cos}\:^{\mathrm{2}} \theta \\ $$$$\Rightarrow\mathrm{4}{q}^{\mathrm{2}} −\mathrm{4}{q}+\mathrm{1}={q}^{\mathrm{4}} −{q}^{\mathrm{5}} \\ $$$$\Rightarrow{q}^{\mathrm{5}} −{q}^{\mathrm{4}} +\mathrm{4}{q}^{\mathrm{2}} −\mathrm{4}{q}+\mathrm{1}=\mathrm{0} \\ $$$${aproximation} \\ $$$$\:\begin{cases}{{q}\approx\mathrm{0}.\mathrm{430159}=\mathrm{cos}\:^{\mathrm{2}} \theta}\\{{q}\approx\mathrm{0}.\mathrm{618033}=\mathrm{cos}\:^{\mathrm{2}} \theta}\end{cases} \\ $$$$ \\ $$