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Question Number 211601    Answers: 0   Comments: 0

set š›‚(2)^(1/3) ,ask Q(š›‚)Upper irreducible cubic equation: x^3 āˆ’3x+1=0 All the roots of

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{set}\:\boldsymbol{\alpha}\sqrt[{\mathrm{3}}]{\mathrm{2}},\mathrm{ask}\:\mathbb{Q}\left(\boldsymbol{\alpha}\right)\mathrm{Upper}\:\mathrm{irreducible}\:\mathrm{cubic}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} āˆ’\mathrm{3}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{All}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$$ \\ $$

Question Number 211598    Answers: 2   Comments: 0

{ ((x^2 āˆ’4x+3<0)),((((2xāˆ’1)/(x+2))ā‰„1)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} āˆ’\mathrm{4}\boldsymbol{{x}}+\mathrm{3}<\mathrm{0}}\\{\frac{\mathrm{2}\boldsymbol{{x}}āˆ’\mathrm{1}}{\boldsymbol{{x}}+\mathrm{2}}\geq\mathrm{1}}\end{cases} \\ $$$$ \\ $$

Question Number 211597    Answers: 1   Comments: 0

2x^4 āˆ’4x^3 āˆ’22x^2 +24x+36=0

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}^{\mathrm{4}} āˆ’\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} āˆ’\mathrm{22}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{x}}+\mathrm{36}=\mathrm{0} \\ $$$$ \\ $$

Question Number 211574    Answers: 1   Comments: 0

{ ((x^2 +y^2 =25)),((x+2yāˆ’3=0)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{25}}\\{\boldsymbol{{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}āˆ’\mathrm{3}=\mathrm{0}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 211548    Answers: 2   Comments: 0

{ ((2x^2 +3y^2 āˆ’6xy=12)),((x^2 āˆ’y^2 =4)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} āˆ’\mathrm{6}\boldsymbol{{x}\mathrm{y}}=\mathrm{12}}\\{\boldsymbol{{x}}^{\mathrm{2}} āˆ’\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{4}}\end{cases} \\ $$$$ \\ $$

Question Number 211535    Answers: 1   Comments: 0

Question Number 211524    Answers: 1   Comments: 0

Solve for x: x^x = 4x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{4x} \\ $$

Question Number 211520    Answers: 2   Comments: 1

determiner les valeurs de pet q sachant que āˆ’2 et 3 sont les āˆ’2 et 3 sont les racines de l equation: 2pqz^2 āˆ’5zāˆ’4(p+q)=0

$$\mathrm{determiner}\:\mathrm{les}\:\mathrm{valeurs}\:\:\mathrm{de}\:\boldsymbol{\mathrm{p}}\mathrm{et}\:\boldsymbol{\mathrm{q}}\:\mathrm{sachant}\:\mathrm{que}\:āˆ’\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\mathrm{sont}\:\mathrm{les}\: \\ $$$$āˆ’\mathrm{2}\:\mathrm{et}\:\mathrm{3}\:\:\mathrm{sont}\:\mathrm{les}\:\mathrm{racines}\:\mathrm{de}\:\mathrm{l}\:\mathrm{equation}: \\ $$$$\mathrm{2}\boldsymbol{\mathrm{pqz}}^{\mathrm{2}} āˆ’\mathrm{5}\boldsymbol{\mathrm{z}}āˆ’\mathrm{4}\left(\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 211509    Answers: 2   Comments: 0

Question Number 211485    Answers: 1   Comments: 0

If ((a āˆ’ b)/c) + ((b āˆ’ c)/a) + ((c + a)/b) = 1 and a āˆ’ b + c ā‰  0 then prove that (1/a) = (1/b) + (1/c) .

$$\mathrm{If}\:\frac{{a}\:āˆ’\:{b}}{{c}}\:+\:\frac{{b}\:āˆ’\:{c}}{{a}}\:+\:\frac{{c}\:+\:{a}}{{b}}\:=\:\mathrm{1}\:\mathrm{and}\: \\ $$$${a}\:āˆ’\:{b}\:+\:{c}\:\neq\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:=\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:. \\ $$

Question Number 211482    Answers: 0   Comments: 0

25^(((1/2) + log_(1/2) 27 + log_(25) 27)) =?

$$\:\mathrm{25}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\:+\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} \mathrm{27}\:+\:{log}_{\mathrm{25}} \mathrm{27}\right)} =? \\ $$

Question Number 211467    Answers: 1   Comments: 0

Solve the following equation āŒŠ x āŒ‹ + (āˆš(x āˆ’(āˆšx) )) = āŒŠ x+ (1/x) āŒ‹ āŒŠ x āŒ‹ is floor of , x ,

$$ \\ $$$$\:\:\:{Solve}\:{the}\:{following}\:{equation} \\ $$$$ \\ $$$$\:\:\:\:\:\lfloor\:{x}\:\rfloor\:+\:\sqrt{{x}\:āˆ’\sqrt{{x}}\:}\:=\:\lfloor\:{x}+\:\frac{\mathrm{1}}{{x}}\:\rfloor \\ $$$$ \\ $$$$\:\:\:\:\:\lfloor\:{x}\:\rfloor\:{is}\:{floor}\:{of}\:,\:\:{x}\:\:,\: \\ $$

Question Number 211451    Answers: 0   Comments: 0

Question Number 211437    Answers: 3   Comments: 1

Question Number 211402    Answers: 1   Comments: 0

Question Number 211398    Answers: 1   Comments: 0

Question Number 211393    Answers: 3   Comments: 1

Question Number 211381    Answers: 2   Comments: 1

Question Number 211377    Answers: 0   Comments: 0

The irrational number ^3 (āˆš(^3 (āˆš2)āˆ’1)) is written as^3 (āˆšp) +^3 (āˆšq) +^3 (āˆšr) what is p, q, r ?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{irrational}}\:\boldsymbol{\mathrm{number}}\: \\ $$$$\:^{\mathrm{3}} \sqrt{\:^{\mathrm{3}} \sqrt{\mathrm{2}}āˆ’\mathrm{1}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{written}}\:\boldsymbol{\mathrm{as}}\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{p}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{q}}}\:+\:^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{r}}}\: \\ $$$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{p}},\:\boldsymbol{\mathrm{q}},\:\boldsymbol{\mathrm{r}}\:? \\ $$

Question Number 211374    Answers: 0   Comments: 0

Evaluate: Ī£_(k=1) ^n (((sin (2^(k+4) Īø))/(sin (2^k Īø)))).

$$\mathrm{Evaluate}:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{sin}\:\left(\mathrm{2}^{{k}+\mathrm{4}} \theta\right)}{\mathrm{sin}\:\left(\mathrm{2}^{\mathrm{k}} \theta\right)}\right). \\ $$

Question Number 211373    Answers: 3   Comments: 0

Question Number 211331    Answers: 2   Comments: 0

x=(((āˆš6)+2+(āˆš3)+(āˆš2))/( (āˆš6)+(āˆš3)āˆ’2āˆ’(āˆš2))) y=(((āˆš6)āˆ’(āˆš3)āˆ’2+(āˆš2))/( (āˆš6)āˆ’(āˆš3)+2āˆ’(āˆš2))) x^5 āˆ’y^5 =?

$$\:\:\:\:\:\mathrm{x}=\frac{\sqrt{\mathrm{6}}+\mathrm{2}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}āˆ’\mathrm{2}āˆ’\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\:\mathrm{y}=\frac{\sqrt{\mathrm{6}}āˆ’\sqrt{\mathrm{3}}āˆ’\mathrm{2}+\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{6}}āˆ’\sqrt{\mathrm{3}}+\mathrm{2}āˆ’\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\mathrm{x}^{\mathrm{5}} āˆ’\mathrm{y}^{\mathrm{5}} \:=?\: \\ $$

Question Number 211330    Answers: 1   Comments: 0

Question Number 211311    Answers: 1   Comments: 0

Dterminer le nombre total des nombres de (3 chiffres)qui sont impair( et) divisibles par 9 compris entre 100 et 500.? formule si c est possible?

$$\boldsymbol{\mathrm{Dterminer}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{nombre}}\:\boldsymbol{\mathrm{total}}\:\:\boldsymbol{\mathrm{des}}\:\boldsymbol{\mathrm{nombres}}\: \\ $$$$\boldsymbol{\mathrm{de}}\:\left(\mathrm{3}\:\boldsymbol{\mathrm{chiffres}}\right)\boldsymbol{\mathrm{qui}}\:\boldsymbol{\mathrm{sont}}\:\boldsymbol{\mathrm{impair}}\left(\:\boldsymbol{\mathrm{et}}\right)\:\boldsymbol{\mathrm{divisibles}}\: \\ $$$$\boldsymbol{\mathrm{par}}\:\mathrm{9}\:\:\:\boldsymbol{\mathrm{compris}}\:\boldsymbol{\mathrm{entre}}\:\mathrm{100}\:\boldsymbol{\mathrm{et}}\:\mathrm{500}.? \\ $$$$\boldsymbol{\mathrm{formule}}\:\boldsymbol{\mathrm{si}}\:\boldsymbol{\mathrm{c}}\:\boldsymbol{\mathrm{est}}\:\boldsymbol{\mathrm{possible}}? \\ $$$$ \\ $$

Question Number 211310    Answers: 1   Comments: 0

Find: LCD(2^(100) āˆ’ 1 ; 2^(120) āˆ’ 1) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{LCD}\left(\mathrm{2}^{\mathrm{100}} \:āˆ’\:\mathrm{1}\:\:;\:\:\mathrm{2}^{\mathrm{120}} \:āˆ’\:\mathrm{1}\right)\:=\:? \\ $$

Question Number 211368    Answers: 1   Comments: 0

soit le systeme d equatiins x+y+z =7 x^2 +y^2 +z^2 =9 xyz =5 (1/x)+(1/y)+(1/z)?

$$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{d}\:\mathrm{equatiins} \\ $$$$\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}\:\:\:\:=\mathrm{7} \\ $$$$\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{9} \\ $$$$\:\:\boldsymbol{\mathrm{xyz}}\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{5} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{z}}}? \\ $$

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