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AlgebraQuestion and Answers: Page 255

Question Number 93963 Answers: 0 Comments: 12

we have for quadratic equations x=((−b±(√(b^2 −4ac)))/(2a)) what about cubic equation is there any rules or ways to solve?

$${we}\:{have}\:{for}\:{quadratic}\:{equations} \\ $$$${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${what}\:{about}\:{cubic}\:{equation}\:{is}\:{there}\:{any} \\ $$$${rules}\:{or}\:{ways}\:{to}\:{solve}? \\ $$

Question Number 93916 Answers: 0 Comments: 2

Question Number 93742 Answers: 0 Comments: 5

No my post option again?? at Tinkutara. because i cannot find my post options again

$$\mathrm{No}\:\mathrm{my}\:\mathrm{post}\:\mathrm{option}\:\mathrm{again}?? \\ $$$$\mathrm{at}\:\mathrm{Tinkutara}. \\ $$$$\mathrm{because}\:\mathrm{i}\:\mathrm{cannot}\:\mathrm{find}\:\mathrm{my}\:\mathrm{post}\:\mathrm{options}\:\mathrm{again} \\ $$

Question Number 93726 Answers: 0 Comments: 1

find the value in sexagesimal numeral system 3° × 15°=? 3 × 15°=?

$${find}\:{the}\:{value}\:{in}\:{sexagesimal}\:{numeral} \\ $$$${system} \\ $$$$\mathrm{3}°\:×\:\mathrm{15}°=? \\ $$$$\mathrm{3}\:×\:\mathrm{15}°=? \\ $$

Question Number 93505 Answers: 0 Comments: 0

Does (x,y)+(x^′ ,y^′ )=(x+x^′ , y+y^′ ) form a vector space? λ(x,y)=(λx,λy)

$$\mathrm{Does} \\ $$$$\left(\mathrm{x},\mathrm{y}\right)+\left(\mathrm{x}^{'} ,\mathrm{y}^{'} \right)=\left(\mathrm{x}+\mathrm{x}^{'} ,\:\mathrm{y}+\mathrm{y}^{'} \right) \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}? \\ $$$$\lambda\left(\mathrm{x},\mathrm{y}\right)=\left(\lambda\mathrm{x},\lambda\mathrm{y}\right) \\ $$

Question Number 93470 Answers: 1 Comments: 4

Solve: 3x^(x + 1) − 3x^(x − 1) = 8

$$\boldsymbol{\mathrm{Solve}}:\:\:\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:−\:\:\mathrm{1}} \:\:\:=\:\:\:\:\mathrm{8} \\ $$

Question Number 93460 Answers: 1 Comments: 1

solve for x,y >0 2x⌊y⌋ = 2020 3y⌊x⌋ = 2021

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\mathrm{y}\:>\mathrm{0} \\ $$$$\mathrm{2}{x}\lfloor\mathrm{y}\rfloor\:=\:\mathrm{2020} \\ $$$$\mathrm{3y}\lfloor{x}\rfloor\:=\:\mathrm{2021}\: \\ $$

Question Number 93446 Answers: 0 Comments: 1

what is the coefficient of x^5 in the expansion (1+x^2 )(1+x)^4

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{5}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} \\ $$

Question Number 93439 Answers: 2 Comments: 0

Question Number 93340 Answers: 1 Comments: 7

Σ_(k = 1) ^(2011) (1/(k(k+1)(k+2))) ?

$$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{2011}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)\left(\mathrm{k}+\mathrm{2}\right)}\:? \\ $$

Question Number 93296 Answers: 1 Comments: 1

Question Number 93177 Answers: 0 Comments: 3

x^2 +(1/x^2 )=47 (√x)+(1/(√x))=...

$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{47} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\sqrt{{x}}}=... \\ $$

Question Number 93173 Answers: 1 Comments: 0

If a_(n + 3) = (a_(n − 1) /a_(n + 1) ) , and a_0 = 1, a_2 = 2 find a_n

$$\mathrm{If}\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{3}} \:\:=\:\:\frac{\mathrm{a}_{\mathrm{n}\:\:−\:\:\mathrm{1}} }{\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} }\:,\:\:\:\:\mathrm{and}\:\:\:\mathrm{a}_{\mathrm{0}} \:\:=\:\:\mathrm{1},\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 93170 Answers: 0 Comments: 2

x^2 +(1/x^2 )=27 (√x)+(1/(√x))=....

$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{27} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\sqrt{{x}}}=.... \\ $$

Question Number 93138 Answers: 2 Comments: 0

{ ((18x^2 =3y(1+9x^2 ))),((18y^2 =3z(1+9y^2 ))),((18z^2 =3x(1+9z^2 ))) :}

$$\begin{cases}{\mathrm{18x}^{\mathrm{2}} =\mathrm{3y}\left(\mathrm{1}+\mathrm{9x}^{\mathrm{2}} \right)}\\{\mathrm{18y}^{\mathrm{2}} =\mathrm{3z}\left(\mathrm{1}+\mathrm{9y}^{\mathrm{2}} \right)}\\{\mathrm{18z}^{\mathrm{2}} =\mathrm{3x}\left(\mathrm{1}+\mathrm{9z}^{\mathrm{2}} \right)}\end{cases} \\ $$

Question Number 93129 Answers: 1 Comments: 2

derive x^2 −(α+β)x+αβ

$${derive}\:{x}^{\mathrm{2}} −\left(\alpha+\beta\right){x}+\alpha\beta \\ $$

Question Number 93057 Answers: 1 Comments: 1

y=b1x1+b2x2+c i need to arrange the equation for thd value of x2

$${y}={b}\mathrm{1}{x}\mathrm{1}+{b}\mathrm{2}{x}\mathrm{2}+{c} \\ $$$${i}\:{need}\:{to}\:{arrange}\:{the}\:{equation}\:{for}\:{thd}\:{value}\:{of}\:{x}\mathrm{2} \\ $$

Question Number 93039 Answers: 0 Comments: 1

{ ((xy+yz = 8)),((yz+xz = 9)),((zx+xy = 5)) :}

$$\begin{cases}{{xy}+{yz}\:=\:\mathrm{8}}\\{{yz}+{xz}\:=\:\mathrm{9}}\\{{zx}+{xy}\:=\:\mathrm{5}}\end{cases} \\ $$

Question Number 93077 Answers: 1 Comments: 1

Se f((√x) −1) = x+6, log[f(1)] = ?

$$\:\:\mathrm{Se}\:\:\mathrm{f}\left(\sqrt{\mathrm{x}}\:−\mathrm{1}\right)\:=\:\mathrm{x}+\mathrm{6},\:\:\mathrm{log}\left[\mathrm{f}\left(\mathrm{1}\right)\right]\:=\:? \\ $$

Question Number 92885 Answers: 0 Comments: 10

Question Number 92880 Answers: 1 Comments: 0

solve 8ϰ+4=3(ϰ−1)+7

$$\mathrm{solve}\:\mathrm{8}\varkappa+\mathrm{4}=\mathrm{3}\left(\varkappa−\mathrm{1}\right)+\mathrm{7} \\ $$

Question Number 92899 Answers: 0 Comments: 1

y=−2.241x+1.585 how do i find value of x by rearranging

$${y}=−\mathrm{2}.\mathrm{241}{x}+\mathrm{1}.\mathrm{585} \\ $$$${how}\:{do}\:{i}\:{find}\:{value}\:{of}\:{x}\:{by}\:{rearranging} \\ $$

Question Number 92839 Answers: 1 Comments: 0

let a is complex number such that a^(10) + a^5 +1 = 0. find a^(2005) + (1/a^(2005) ) ?

$$\mathrm{let}\:\mathrm{a}\:\mathrm{is}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{10}} \:+\:\mathrm{a}^{\mathrm{5}} \:+\mathrm{1}\:=\:\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{a}^{\mathrm{2005}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2005}} }\:? \\ $$

Question Number 92835 Answers: 0 Comments: 3

Question Number 92831 Answers: 1 Comments: 5

Question Number 92820 Answers: 1 Comments: 0

a convergent geometric sequence with first term a is such that the sum of the terms after the n^(th) term is three times the n^(th) term, find the common ratio and show that its sum to infinity is 4a.

$${a}\:{convergent}\:{geometric}\:{sequence}\:{with} \\ $$$${first}\:{term}\:{a}\:{is}\:{such}\:{that}\:{the}\:{sum}\:{of} \\ $$$${the}\:{terms}\:{after}\:{the}\:{n}^{{th}} \:{term}\:{is} \\ $$$${three}\:{times}\:{the}\:{n}^{{th}} \:{term},\:{find}\:{the} \\ $$$${common}\:{ratio}\:{and}\:{show}\:{that}\:{its}\: \\ $$$${sum}\:{to}\:{infinity}\:{is}\:\mathrm{4}{a}. \\ $$

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