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AlgebraQuestion and Answers: Page 93

Question Number 174062    Answers: 2   Comments: 2

find all prime p and q such that p^2 − p = 37q^2 − q

$$\mathrm{find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\:\mathrm{such}\:\mathrm{that}\:\:\:\:\mathrm{p}^{\mathrm{2}} \:\:−\:\:\mathrm{p}\:\:\:\:=\:\:\:\mathrm{37q}^{\mathrm{2}} \:\:−\:\:\mathrm{q} \\ $$

Question Number 174059    Answers: 2   Comments: 3

if x^3 +y^3 +3xy=1, then x+y=?

$${if}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{3}{xy}=\mathrm{1},\:{then}\:{x}+{y}=? \\ $$

Question Number 174057    Answers: 0   Comments: 1

Question Number 174036    Answers: 1   Comments: 0

Factorize x^2 + (√(2x ))+ x + 2

$$\:\:\mathrm{Factorize}\:{x}^{\mathrm{2}} \:+\:\sqrt{\mathrm{2}{x}\:}+\:{x}\:+\:\mathrm{2} \\ $$

Question Number 174029    Answers: 1   Comments: 1

x+y=1 x^5 +xy+y^5 =x^2 y^(2 ) faind the volue of x^(2022) +xy+y^(2022) =?

$${x}+{y}=\mathrm{1} \\ $$$${x}^{\mathrm{5}} +{xy}+{y}^{\mathrm{5}} ={x}^{\mathrm{2}} {y}^{\mathrm{2}\:\:\:\:\:\:} \\ $$$${faind}\:{the}\:{volue}\:{of}\:\:\:{x}^{\mathrm{2022}} +{xy}+{y}^{\mathrm{2022}} =? \\ $$

Question Number 174023    Answers: 2   Comments: 1

Question Number 173997    Answers: 2   Comments: 0

If (x)^(1/3) − 3 = ((x−36))^(1/3) then ((x^( 2) −1)/x) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{If}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{{x}}\:−\:\mathrm{3}\:=\:\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{x}^{\:\mathrm{2}} −\mathrm{1}}{{x}}\:=\:?\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 173992    Answers: 1   Comments: 1

Question Number 173984    Answers: 0   Comments: 0

Question Number 173981    Answers: 2   Comments: 0

Question Number 173978    Answers: 1   Comments: 0

Solve system of equations: x+((3x−y)/(x^2 +y^2 ))=3 y−((x+3y)/(x^2 +y^2 ))=0

$$\mathrm{Solve}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\mathrm{x}+\frac{\mathrm{3x}−\mathrm{y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{3} \\ $$$$\mathrm{y}−\frac{\mathrm{x}+\mathrm{3y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{0} \\ $$$$ \\ $$

Question Number 173970    Answers: 1   Comments: 3

Question Number 173948    Answers: 1   Comments: 4

Question Number 173946    Answers: 1   Comments: 0

If 3sin(x)+4cos(y)−3sin(y)=8 then .. sin(x) + sin(y)=?

$$ \\ $$$$\:\:\:{If}\:\mathrm{3}{sin}\left({x}\right)+\mathrm{4}{cos}\left({y}\right)−\mathrm{3}{sin}\left({y}\right)=\mathrm{8} \\ $$$$\:\:\:{then}\:..\:\:\:\:{sin}\left({x}\right)\:+\:{sin}\left({y}\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 173933    Answers: 1   Comments: 1

Question Number 173958    Answers: 0   Comments: 0

Question Number 173926    Answers: 2   Comments: 3

Q: a_( n ) is an arithmatic sequence. a ( first term) and d (difference ) such that , a_( a) + a_( d) = a_( ad) find : a_( n) =? note: a , d ∈ N

$$ \\ $$$$\:\:\:\:\:{Q}: \\ $$$$\:\:\:\:\:\:\:{a}_{\:{n}\:} \:\:{is}\:{an}\:{arithmatic}\:{sequence}. \\ $$$$\:\:\:\:\:\:\:\:\:\:{a}\:\left(\:{first}\:{term}\right)\:{and}\:\:{d}\:\left({difference}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:{such}\:{that}\:,\:\:{a}_{\:{a}} \:+\:{a}_{\:{d}} \:=\:{a}_{\:{ad}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{find}\:\:\::\:\:\:\:{a}_{\:{n}} \:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:{note}:\:\:{a}\:\:,\:\:{d}\:\:\:\in\:\mathbb{N}\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 173923    Answers: 1   Comments: 1

Question Number 173917    Answers: 0   Comments: 2

prove: (−1)!

$${prove}: \\ $$$$\left(−\mathrm{1}\right)! \\ $$

Question Number 173956    Answers: 0   Comments: 1

Question Number 173889    Answers: 0   Comments: 1

the anser is the folowing

$${the}\:{anser}\:{is}\:{the}\:{folowing} \\ $$

Question Number 173887    Answers: 0   Comments: 0

Question Number 173882    Answers: 0   Comments: 0

Question Number 173871    Answers: 0   Comments: 1

2^x ∙3^y =4 2^y ∙3^x =6 prove that xy=z(z+1) 6^z =2

$$\mathrm{2}^{{x}} \centerdot\mathrm{3}^{{y}} =\mathrm{4} \\ $$$$\mathrm{2}^{{y}} \centerdot\mathrm{3}^{{x}} =\mathrm{6}\:\:\:\:\:\:\:{prove}\:{that}\:\:{xy}={z}\left({z}+\mathrm{1}\right) \\ $$$$\mathrm{6}^{{z}} =\mathrm{2} \\ $$

Question Number 173869    Answers: 2   Comments: 2

If, ( (((√(10)) +(√6)+2)/( (√5) −(√(3 )) + (√2))) )^( 2) = a + (√b) then. a , b = ?

$$ \\ $$$$\:{If},\:\:\:\left(\:\frac{\sqrt{\mathrm{10}}\:+\sqrt{\mathrm{6}}+\mathrm{2}}{\:\sqrt{\mathrm{5}}\:−\sqrt{\mathrm{3}\:}\:+\:\sqrt{\mathrm{2}}}\:\right)^{\:\mathrm{2}} =\:{a}\:+\:\sqrt{{b}} \\ $$$$\:\:\:\:\:\:\:\:{then}.\:\:\:\:\:\:\:\:{a}\:\:,\:\:\:{b}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 173864    Answers: 0   Comments: 0

(√x) ≥ ((x^4 −2x^3 +2x−1)/(x^3 −2x^2 +2x))

$$\:\:\:\:\sqrt{{x}}\:\geqslant\:\frac{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}} \\ $$

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