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AlgebraQuestion and Answers: Page 263

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.

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

Question Number 92778 Answers: 0 Comments: 1

Question Number 92727 Answers: 1 Comments: 0

Solve: x^y = y^x ....... (i) 3^x = 15^y ...... (ii) x ≠ y, x, y ∈ R

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:=\:\:\mathrm{y}^{\mathrm{x}} \:\:\:\:\:.......\:\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{x}} \:\:=\:\:\mathrm{15}^{\mathrm{y}} \:\:\:\:......\:\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\mathrm{x}\:\:\neq\:\:\mathrm{y},\:\:\:\:\:\:\:\mathrm{x},\:\:\mathrm{y}\:\in\:\mathbb{R} \\ $$

Question Number 92717 Answers: 2 Comments: 5

Question Number 92608 Answers: 0 Comments: 4

Question Number 92566 Answers: 0 Comments: 2

Posting Question with Images Preferably you should type the question. However if you are using pictures then please do the following steps which posting a photo of printed question. A. Use camscanner app to take pictures (search for camscanner in playstore). B. Crop picture so that you only have specifc question that you want to ask in the image.

$$\mathrm{Posting}\:\mathrm{Question}\:\mathrm{with}\:\mathrm{Images} \\ $$$$\mathrm{Preferably}\:\mathrm{you}\:\mathrm{should}\:\mathrm{type}\:\mathrm{the}\:\mathrm{question}. \\ $$$$\mathrm{However}\:\mathrm{if}\:\mathrm{you}\:\mathrm{are}\:\mathrm{using}\:\mathrm{pictures}\:\mathrm{then} \\ $$$$\mathrm{please}\:\mathrm{do}\:\mathrm{the}\:\mathrm{following}\:\mathrm{steps} \\ $$$$\mathrm{which}\:\mathrm{posting}\:\mathrm{a}\:\mathrm{photo}\:\mathrm{of}\:\mathrm{printed} \\ $$$$\mathrm{question}. \\ $$$$\mathrm{A}.\:\mathrm{Use}\:\mathrm{camscanner}\:\mathrm{app}\:\mathrm{to}\:\mathrm{take}\: \\ $$$$\mathrm{pictures}\:\left(\mathrm{search}\:\mathrm{for}\:\mathrm{camscanner}\:\mathrm{in}\right. \\ $$$$\left.\mathrm{playstore}\right).\: \\ $$$$\mathrm{B}.\:\mathrm{Crop}\:\mathrm{picture}\:\mathrm{so}\:\mathrm{that}\:\mathrm{you}\:\mathrm{only} \\ $$$$\mathrm{have}\:\mathrm{specifc}\:\mathrm{question}\:\mathrm{that}\:\mathrm{you}\:\mathrm{want} \\ $$$$\mathrm{to}\:\mathrm{ask}\:\mathrm{in}\:\mathrm{the}\:\mathrm{image}. \\ $$$$ \\ $$

Question Number 92557 Answers: 0 Comments: 3

If a_1 = 5, a_2 = 13 and a_(n + 2) = 5a_(n + 1) − 6a_n . Find a_n

$$\mathrm{If}\:\:\:\mathrm{a}_{\mathrm{1}} \:\:=\:\:\mathrm{5},\:\:\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{13}\:\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \:\:\:=\:\:\mathrm{5a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} \:−\:\:\mathrm{6a}_{\mathrm{n}} . \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 92489 Answers: 0 Comments: 0

(3+((cq)/(12b)))s^2 +((6c)/b)s+(((8c^2 )/(3b^2 ))−b)=0 (1+((cq)/(4b)))s^2 +((3c)/b)(1−((cq)/(12b)))s+(((12c^2 )/b^2 )−b)=0 solve simultaneously for q and s in terms of b and c.

$$\left(\mathrm{3}+\frac{{cq}}{\mathrm{12}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{6}{c}}{{b}}{s}+\left(\frac{\mathrm{8}{c}^{\mathrm{2}} }{\mathrm{3}{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$$\left(\mathrm{1}+\frac{{cq}}{\mathrm{4}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{3}{c}}{{b}}\left(\mathrm{1}−\frac{{cq}}{\mathrm{12}{b}}\right){s}+\left(\frac{\mathrm{12}{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$${solve}\:{simultaneously}\:{for}\:\boldsymbol{{q}}\:{and}\:\boldsymbol{{s}} \\ $$$${in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$

Question Number 92488 Answers: 0 Comments: 11

(3x)^(log_b 3) = (5x)^(log_b 5) x = ?

$$\:\left(\mathrm{3x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{3}} \:=\:\left(\mathrm{5x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{5}} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 92448 Answers: 4 Comments: 1

{ ((5^x .6^y = 150)),((5^y .6^x = 180 )) :}

$$\begin{cases}{\mathrm{5}^{\mathrm{x}} .\mathrm{6}^{\mathrm{y}} \:=\:\mathrm{150}}\\{\mathrm{5}^{\mathrm{y}} .\mathrm{6}^{\mathrm{x}} \:=\:\mathrm{180}\:}\end{cases} \\ $$

Question Number 92426 Answers: 0 Comments: 4

If x^2 +2xy=0 find y

$$\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}=\mathrm{0}\:\mathrm{find}\:\mathrm{y} \\ $$

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