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AlgebraQuestion and Answers: Page 336

Question Number 36110 Answers: 0 Comments: 0

{Δ1 3 6 / ×<⌈+2/ 47

$$\left\{\Delta\mathrm{1}\:\mathrm{3}\:\mathrm{6}\:/\:×<\lceil+\mathrm{2}/\right. \\ $$$$\mathrm{47} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 36019 Answers: 3 Comments: 0

If a+b+c=0 show that ((a/(b−c))+(b/(c−a))+(c/(a−b)))(((b−c)/a)+((c−a)/b) +((a−b)/c))=9

$${If}\:{a}+{b}+{c}=\mathrm{0}\:{show}\:{that} \\ $$$$\left(\frac{{a}}{{b}−{c}}+\frac{{b}}{{c}−{a}}+\frac{{c}}{{a}−{b}}\right)\left(\frac{{b}−{c}}{{a}}+\frac{{c}−{a}}{{b}}\:+\frac{{a}−{b}}{{c}}\right)=\mathrm{9} \\ $$

Question Number 35892 Answers: 2 Comments: 2

Question Number 35768 Answers: 0 Comments: 0

Question Number 35723 Answers: 1 Comments: 0

Find the largest prime factor of the following: (1×2×3)+(2×3×4)+...+(2014×2015×2016)

$${Find}\:{the}\:{largest}\:{prime}\:{factor}\:{of}\:\:{the}\:{following}: \\ $$$$\left(\mathrm{1}×\mathrm{2}×\mathrm{3}\right)+\left(\mathrm{2}×\mathrm{3}×\mathrm{4}\right)+...+\left(\mathrm{2014}×\mathrm{2015}×\mathrm{2016}\right) \\ $$

Question Number 35626 Answers: 0 Comments: 0

1) study the diagonalisstion of the matrice A = (((1+a^2 a 0)),((a 1+a^2 a)) ) ( 0 a 1+a^2 ) 2) calculate A^n

$$\left.\mathrm{1}\right)\:{study}\:{the}\:{diagonalisstion}\:{of}\:{the}\:{matrice} \\ $$$${A}\:=\begin{pmatrix}{\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}\:\:\:\:\:\:\:\mathrm{0}}\\{{a}\:\:\:\:\:\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:{a}\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$

Question Number 35622 Answers: 0 Comments: 0

find all matrices M ∈M_3 (R) / M^2 =M

$${find}\:{all}\:{matrices}\:{M}\:\in{M}_{\mathrm{3}} \left({R}\right)\:\:/\:\:{M}^{\mathrm{2}} \:={M} \\ $$

Question Number 35481 Answers: 1 Comments: 1

if x^p y^p =(x + y)^(p +q) prove that (dy/dx)=(y/x)

$${if}\:{x}^{{p}} {y}^{{p}} =\left({x}\:+\:{y}\right)\:^{{p}\:+{q}} \:\:\: \\ $$$${prove}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$

Question Number 35475 Answers: 1 Comments: 0

Is Rational Number Countable? If yes how do we count it with one to one correspondence with set of natural number N?

$${Is}\:{Rational}\:{Number}\:{Countable}? \\ $$$${If}\:{yes}\:{how}\:{do}\:{we}\:{count}\:{it}\:{with}\:{one}\:{to}\:{one}\:{correspondence}\:{with}\:{set}\:{of}\:{natural}\:{number}\:\mathbb{N}? \\ $$

Question Number 35345 Answers: 0 Comments: 0

yes (√2)x^2

$${yes}\:\sqrt{\mathrm{2}}{x}^{\mathrm{2}} \\ $$

Question Number 35338 Answers: 0 Comments: 1

((14x^2 +16)/(21))−((2x^2 +8)/(8x^2 −11))=((2x^2 )/3)

$$\frac{\mathrm{14}{x}^{\mathrm{2}} +\mathrm{16}}{\mathrm{21}}−\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{8}}{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{11}}=\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{3}} \\ $$

Question Number 35336 Answers: 2 Comments: 1

(√(2x^2 ))+7x+5(√2)=0

$$\sqrt{\mathrm{2}{x}^{\mathrm{2}} }+\mathrm{7}{x}+\mathrm{5}\sqrt{\mathrm{2}}=\mathrm{0} \\ $$

Question Number 35291 Answers: 1 Comments: 1

solve in Z x^3 +6y^3 =4z^3

$${solve}\:\:{in}\:{Z}\:\:{x}^{\mathrm{3}} +\mathrm{6}{y}^{\mathrm{3}} =\mathrm{4}{z}^{\mathrm{3}} \\ $$

Question Number 35256 Answers: 1 Comments: 1

Factorize :x^5 −y^5

$$\mathrm{Factorize}\::\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \\ $$

Question Number 35153 Answers: 1 Comments: 0

Question Number 35152 Answers: 0 Comments: 2

Question Number 35080 Answers: 2 Comments: 0

If (a/(b+c)) +(b/(c+a)) +(c/(a+b))=1 then prove that (a^2 /(b+c)) +(b^2 /(c+a)) +(c^2 /(a+b))=0

$${If}\:\frac{{a}}{{b}+{c}}\:+\frac{{b}}{{c}+{a}}\:+\frac{{c}}{{a}+{b}}=\mathrm{1}\:{then}\:{prove}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} }{{b}+{c}}\:+\frac{{b}^{\mathrm{2}} }{{c}+{a}}\:+\frac{{c}^{\mathrm{2}} }{{a}+{b}}=\mathrm{0} \\ $$

Question Number 35056 Answers: 0 Comments: 2

let p(x)=(1+jx)^n −(1−jx)^n 1) find the roots of p(x) 2)factorize p(x) inside C[x] j =e^(i((2π)/3)) .

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} \:−\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:. \\ $$

Question Number 34870 Answers: 3 Comments: 4

Question Number 34760 Answers: 2 Comments: 0

Question Number 34739 Answers: 3 Comments: 3

Question Number 34738 Answers: 0 Comments: 2

Question Number 34686 Answers: 0 Comments: 0

decompose F(x) = (((2n)!)/((x^2 −1)(x^2 −2)....(x^2 −n)))

$${decompose}\:{F}\left({x}\right)\:\:=\:\frac{\left(\mathrm{2}{n}\right)!}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{2}} \:−\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:−{n}\right)} \\ $$

Question Number 34685 Answers: 0 Comments: 0

decompose the fraction F(x)= (1/((x+2)( x^n −1))) with n ∈ N^★

$${decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}}{\left({x}+\mathrm{2}\right)\left(\:{x}^{{n}} \:\:−\mathrm{1}\right)}\:\:{with}\:{n}\:\in\:{N}^{\bigstar} \\ $$

Question Number 34680 Answers: 0 Comments: 0

decompose inside C(x) the fraction F(x) = (x^2 /(x^4 −2x^2 cos(2a) +1)) .

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\:\:\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} {cos}\left(\mathrm{2}{a}\right)\:+\mathrm{1}}\:. \\ $$

Question Number 34673 Answers: 0 Comments: 0

solve (((1+iz)/(1−iz)))^n = ((1+itanα)/(1−itanα)) with −(π/2)<α<(π/2)

$${solve}\:\left(\frac{\mathrm{1}+{iz}}{\mathrm{1}−{iz}}\right)^{{n}} \:=\:\frac{\mathrm{1}+{itan}\alpha}{\mathrm{1}−{itan}\alpha}\:\:{with}\:−\frac{\pi}{\mathrm{2}}<\alpha<\frac{\pi}{\mathrm{2}} \\ $$

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