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AlgebraQuestion and Answers: Page 226

Question Number 131688 Answers: 2 Comments: 0

Let α and β are the roots of the equation x^2 −6x−2=0. If a_n = α^n −β^n for n ≥1 then the value of ((a_(10) −2a_8 )/(2a_9 )) ?

$$\:\mathrm{Let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} −\mathrm{6x}−\mathrm{2}=\mathrm{0}. \\ $$$$\mathrm{If}\:{a}_{{n}} \:=\:\alpha^{{n}} −\beta^{{n}} \:\mathrm{for}\:{n}\:\geqslant\mathrm{1}\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{{a}_{\mathrm{10}} −\mathrm{2}{a}_{\mathrm{8}} }{\mathrm{2}{a}_{\mathrm{9}} }\:? \\ $$

Question Number 131640 Answers: 1 Comments: 0

Question Number 131605 Answers: 2 Comments: 0

solve the equation m^4 −7m^3 + 14m^2 −7m + 1 = 0

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:{m}^{\mathrm{4}} −\mathrm{7}{m}^{\mathrm{3}} +\:\mathrm{14}{m}^{\mathrm{2}} −\mathrm{7}{m}\:+\:\mathrm{1}\:=\:\mathrm{0}\: \\ $$

Question Number 131480 Answers: 0 Comments: 0

what are the condition for absolute inequality?

$${what}\:{are}\:{the}\:{condition}\:{for}\:{absolute}\: \\ $$$${inequality}? \\ $$

Question Number 131440 Answers: 0 Comments: 2

∣2x+7∣<−2 solve=?

$$\mid\mathrm{2}{x}+\mathrm{7}\mid<−\mathrm{2}\:\:\:\:\:\:{solve}=? \\ $$

Question Number 131430 Answers: 2 Comments: 2

(((((x^x )^x ))^(1/(1/x)) ))^(1/(1/x)) =4 find x=?

$$\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left(\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left.{x}\:^{{x}} \right)^{{x}} }\right.}=\mathrm{4}\:\:\:\:\:\:\:{find}\:\:{x}=? \\ $$

Question Number 131421 Answers: 0 Comments: 1

Solve using trig method 8x^3 −4x^2 −4x+1=0

$$\mathrm{Solve}\:\mathrm{using}\:\mathrm{trig}\:\mathrm{method} \\ $$$$\:\:\mathrm{8x}^{\mathrm{3}} −\mathrm{4x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 131390 Answers: 0 Comments: 0

Question Number 131374 Answers: 3 Comments: 0

Question Number 131363 Answers: 0 Comments: 2

Question Number 131343 Answers: 1 Comments: 0

A mapping is defined as G→S where (G,×) and (S,+), show that the mapping f(x) = ln x is an isomophism.

$$\mathrm{A}\:\mathrm{mapping}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}\:{G}\rightarrow{S}\:\mathrm{where}\:\left({G},×\right)\:\mathrm{and}\:\left({S},+\right), \\ $$$$\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{mapping}\:{f}\left({x}\right)\:=\:\mathrm{ln}\:{x}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isomophism}. \\ $$

Question Number 131309 Answers: 2 Comments: 0

Question Number 131218 Answers: 2 Comments: 0

Question Number 131214 Answers: 1 Comments: 0

Question Number 131201 Answers: 2 Comments: 0

Question Number 131158 Answers: 1 Comments: 0

If 4a_n +2a_(−n) =3n^2 +2n−3 find a_n =?

$${If}\:\mathrm{4}{a}_{{n}} +\mathrm{2}{a}_{−{n}} =\mathrm{3}{n}^{\mathrm{2}} +\mathrm{2}{n}−\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:=? \\ $$

Question Number 131155 Answers: 2 Comments: 0

Given { ((a_(n+2) =a_(n+1) +(1/2)a_n )),((a_1 =3 ; a_2 =2)) :} find a_n .

$${Given}\:\begin{cases}{{a}_{{n}+\mathrm{2}} ={a}_{{n}+\mathrm{1}} +\frac{\mathrm{1}}{\mathrm{2}}{a}_{{n}} }\\{{a}_{\mathrm{1}} =\mathrm{3}\:;\:{a}_{\mathrm{2}} =\mathrm{2}}\end{cases} \\ $$$$\:{find}\:{a}_{{n}} . \\ $$

Question Number 206939 Answers: 1 Comments: 7

In how many ways can the word KINECTIC be arranged so that no vowels can be together?

Question Number 131084 Answers: 2 Comments: 0

let solve this in R : x^4 −x^3 −4x^2 +x+1=0.

$$\mathrm{let}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{in}\:\mathbb{R}\::\: \\ $$$${x}^{\mathrm{4}} −{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0}. \\ $$

Question Number 131075 Answers: 1 Comments: 0

If a−3=−b−4=−c−5=d+6=e+7= a−b−c+d+e+8 then a−b−c+d+e =?

$$\mathrm{If}\:\mathrm{a}−\mathrm{3}=−\mathrm{b}−\mathrm{4}=−\mathrm{c}−\mathrm{5}=\mathrm{d}+\mathrm{6}=\mathrm{e}+\mathrm{7}= \\ $$$$\mathrm{a}−\mathrm{b}−\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{8}\:\mathrm{then}\:\mathrm{a}−\mathrm{b}−\mathrm{c}+\mathrm{d}+\mathrm{e}\:=? \\ $$

Question Number 131064 Answers: 3 Comments: 0

Question Number 131016 Answers: 0 Comments: 0

Question Number 130853 Answers: 1 Comments: 0

Question Number 130846 Answers: 1 Comments: 1

prove that 3sec^(−1) ((√2))−4csc^(−1) ((√2))+5cot^(−1) (2)=1.533

$${prove}\:{that} \\ $$$$\mathrm{3}{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{2}}\right)−\mathrm{4}{csc}^{−\mathrm{1}} \left(\sqrt{\mathrm{2}}\right)+\mathrm{5}{cot}^{−\mathrm{1}} \left(\mathrm{2}\right)=\mathrm{1}.\mathrm{533} \\ $$

Question Number 130806 Answers: 1 Comments: 0

Question Number 130802 Answers: 2 Comments: 0

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