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AlgebraQuestion and Answers: Page 348

Question Number 26733    Answers: 1   Comments: 1

Question Number 27002    Answers: 2   Comments: 4

Question Number 26694    Answers: 1   Comments: 0

divide x^6 −y^6 by the product of x^2 +x^ y+y^(2 ) and x−y.

$${divide}\:{x}^{\mathrm{6}} −{y}^{\mathrm{6}} \:{by}\:{the}\:{product}\:{of}\:{x}^{\mathrm{2}} +{x}^{} {y}+{y}^{\mathrm{2}\:} \:{and}\:{x}−{y}. \\ $$

Question Number 26680    Answers: 1   Comments: 0

(b−c)x^2 +(c−a)x+(a−b)=0 if the eqation roots are eqal you proved that 2b=a+c.

$$\left({b}−{c}\right){x}^{\mathrm{2}} +\left({c}−{a}\right){x}+\left({a}−{b}\right)=\mathrm{0}\:{if}\:{the}\: \\ $$$${eqation}\:{roots}\:\:{are}\:{eqal}\:{you}\:{proved}\:{that} \\ $$$$\mathrm{2}{b}={a}+{c}. \\ $$

Question Number 26642    Answers: 2   Comments: 0

9x^2 +41x−204=0. solved it.

$$\mathrm{9}{x}^{\mathrm{2}} +\mathrm{41}{x}−\mathrm{204}=\mathrm{0}.\:{solved}\:{it}. \\ $$

Question Number 26638    Answers: 1   Comments: 0

x^3 −8x^2 +7 factorise it.

$$\mathrm{x}^{\mathrm{3}} −\mathrm{8x}^{\mathrm{2}} +\mathrm{7}\:\:\mathrm{factorise}\:\mathrm{it}. \\ $$

Question Number 26583    Answers: 0   Comments: 2

find the decomposition in C[x] then R[x] for the rationsl fraction F(x)= ((1 )/(x^(2n) −1)) .with n integer not 0

$${find}\:{the}\:{decomposition}\:{in}\:\mathbb{C}\left[{x}\right]\:{then}\:\mathbb{R}\left[{x}\right] \\ $$$${for}\:{the}\:{rationsl}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}\:}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:\:.{with}\:{n}\:{integer}\:{not}\:\mathrm{0} \\ $$

Question Number 26582    Answers: 0   Comments: 1

p is a polynomial having the roots x_1 ,x_2 ,...x_n with x_i ≠ x_j fori≠j give the decomposition of the fravtion F(x)= ((p^′ (x))/(p(x)))

$${p}\:{is}\:{a}\:{polynomial}\:{having}\:{the}\:{roots}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...{x}_{{n}} \\ $$$${with}\:{x}_{{i}} \neq\:{x}_{{j}} \:{fori}\neq{j}\:{give}\:{the}\:{decomposition} \\ $$$${of}\:{the}\:{fravtion}\:{F}\left({x}\right)=\:\frac{{p}^{'} \left({x}\right)}{{p}\left({x}\right)} \\ $$

Question Number 29176    Answers: 3   Comments: 1

∫sec x dx=?

$$\int{sec}\:{x}\:{dx}=? \\ $$

Question Number 26461    Answers: 0   Comments: 1

Question Number 26405    Answers: 1   Comments: 0

Question Number 26348    Answers: 1   Comments: 1

Question Number 26347    Answers: 0   Comments: 0

solve: 5x(1 + (1/(x^2 + y^2 ))) = 12 ..... equation (i) 5y(1 − (1/(x^2 + y^2 ))) = 4 ...... equation (ii)

$$\mathrm{solve}: \\ $$$$\mathrm{5x}\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\right)\:=\:\mathrm{12}\:\:\:\:\:\:\:\:.....\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{5y}\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\right)\:=\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:......\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 26274    Answers: 0   Comments: 2

could there be an analytical or numerical meghod for solving this non-linear simultaneous equation x+y=5 x^x +y^y =31 please help if possible

$${could}\:{there}\:{be}\:{an}\:{analytical}\:{or} \\ $$$${numerical}\:{meghod}\:{for}\:{solving} \\ $$$${this}\:{non}-{linear}\:{simultaneous} \\ $$$${equation} \\ $$$${x}+{y}=\mathrm{5} \\ $$$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$$ \\ $$$${please}\:{help}\:{if}\:{possible} \\ $$

Question Number 26269    Answers: 1   Comments: 0

if x^x =2 what is the value of x?

$${if}\:{x}^{{x}} =\mathrm{2}\:{what}\:{is}\:{the}\:{value}\:{of}\:{x}? \\ $$

Question Number 26250    Answers: 1   Comments: 0

someone should help witb solution please x^3 +y^3 =3x^2 −6x−3y+4 x^2 −y^2 −6x+y−10=(√((y+5)))−(√((4x+y)))

$${someone}\:{should}\:{help}\:{witb}\:{solution}\:{please} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{3}{y}+\mathrm{4} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{6}{x}+{y}−\mathrm{10}=\sqrt{\left({y}+\mathrm{5}\right)}−\sqrt{\left(\mathrm{4}{x}+{y}\right)} \\ $$

Question Number 26235    Answers: 1   Comments: 0

Find the real root of x^2 +(1/x)=c .

$${Find}\:{the}\:{real}\:{root}\:{of} \\ $$$$\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}}={c}\:. \\ $$

Question Number 26229    Answers: 1   Comments: 1

after factorise (x2+2x+1)we get

$$\mathrm{after}\:\mathrm{factorise}\:\left(\mathrm{x2}+\mathrm{2x}+\mathrm{1}\right)\mathrm{we}\:\mathrm{get} \\ $$

Question Number 26228    Answers: 0   Comments: 1

if x^4 +(1/x^4 )=322 find x^3 −(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{322}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26227    Answers: 1   Comments: 0

if x^2 +(1/x^2 )=98 find x^3 +(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{98}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26224    Answers: 1   Comments: 1

find the value of x−(1/x).when x^4 +(1/x^4 )=332

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}.\mathrm{when}\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{332} \\ $$

Question Number 26218    Answers: 0   Comments: 2

∫_2 ^4 sinθ dθ

$$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\mathrm{sin}\theta\:{d}\theta \\ $$

Question Number 26207    Answers: 1   Comments: 0

I think of a two digit number.The sum of the digits is 9. When the number is reversed and subtracted from the original, the result is 45. Find the original number

$$\mathrm{I}\:\mathrm{think}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}.\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{9}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reversed}\:\mathrm{and}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{original},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{45}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number} \\ $$

Question Number 26153    Answers: 1   Comments: 0

ratio of income of two persons is 9 is to 7.ratio of their expenses is 4 is to 3 .every person saves rupees 200. find income of each.

$${ratio}\:{of}\:{income}\:{of}\:{two}\:{persons}\:{is} \\ $$$$\mathrm{9}\:{is}\:{to}\:\mathrm{7}.{ratio}\:{of}\:{their}\:{expenses} \\ $$$${is}\:\mathrm{4}\:{is}\:{to}\:\mathrm{3}\:.{every}\:{person}\:{saves}\: \\ $$$${rupees}\:\mathrm{200}.\:{find}\:{income}\:{of}\:{each}. \\ $$

Question Number 26147    Answers: 1   Comments: 0

There are 5 more girls than boys in a class. If 2 boys join the class, the ratio of girls to boys will be 5:4. Find the number of of girls in the class.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{5}\:\mathrm{more}\:\mathrm{girls}\:\mathrm{than}\:\mathrm{boys}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}.\:\mathrm{If}\:\mathrm{2}\:\mathrm{boys}\:\mathrm{join} \\ $$$$\mathrm{the}\:\mathrm{class},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{girls}\:\mathrm{to}\:\mathrm{boys}\:\mathrm{will}\:\mathrm{be}\:\mathrm{5}:\mathrm{4}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{of}\:\mathrm{girls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}. \\ $$

Question Number 26143    Answers: 2   Comments: 1

2000^(3000) vs 3000^(2000) who is stronger ?

$$\mathrm{2000}^{\mathrm{3000}} \:\:\boldsymbol{{vs}}\:\mathrm{3000}^{\mathrm{2000}} \\ $$$$ \\ $$$$\:\boldsymbol{{who}}\:\boldsymbol{{is}}\:\boldsymbol{{stronger}}\:? \\ $$

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