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Question Number 132358    Answers: 0   Comments: 2

find the equation whose roots are α and β. find α and β if α−β=2 and α^2 −β^2 =3

$${find}\:{the}\:{equation}\:{whose}\:{roots}\:{are} \\ $$$$\alpha\:{and}\:\beta.\:{find}\:\alpha\:{and}\:\beta\:{if}\:\:\alpha−\beta=\mathrm{2}\:{and}\:\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} =\mathrm{3} \\ $$

Question Number 132295    Answers: 0   Comments: 4

Question Number 132285    Answers: 2   Comments: 0

Simplify the equation of (((x^(1/3) −x^(1/6) )(x^(1/2) +x)(x^(1/2) +x^(1/3) +x^(2/3) ))/((x^(4/3) −x)(x+x^(1/3) +x^(2/3) ))) with x ≠ 0

$$\mathrm{Simplify}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\: \\ $$$$\frac{\left(\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{6}}} \right)\left(\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{x}\right)\left(\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)}{\left(\mathrm{x}^{\frac{\mathrm{4}}{\mathrm{3}}} −\mathrm{x}\right)\left(\mathrm{x}+\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)} \\ $$$$\mathrm{with}\:\mathrm{x}\:\neq\:\mathrm{0} \\ $$$$ \\ $$

Question Number 132260    Answers: 1   Comments: 0

Question Number 132257    Answers: 1   Comments: 0

Question Number 132198    Answers: 2   Comments: 0

If { ((16^(a+b) = ((√2)/2))),((16^(b+c) = 2)),((16^(a+c) = 2(√2))) :} then c = __

$$\mathrm{If}\:\begin{cases}{\mathrm{16}^{{a}+{b}} \:=\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\\{\mathrm{16}^{{b}+{c}} \:=\:\mathrm{2}}\\{\mathrm{16}^{{a}+{c}} \:=\:\mathrm{2}\sqrt{\mathrm{2}}}\end{cases} \\ $$$$\:\mathrm{then}\:\mathrm{c}\:=\:\_\_\: \\ $$

Question Number 132180    Answers: 1   Comments: 0

solve : 2sec^2 x+(2(√2)−3)secx−3(√2)=0 ; 0≤x≤(π/4)

$${solve}\:: \\ $$$$\mathrm{2}{sec}^{\mathrm{2}} {x}+\left(\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{3}\right){secx}−\mathrm{3}\sqrt{\mathrm{2}}=\mathrm{0}\:;\:\mathrm{0}\leqslant{x}\leqslant\frac{\pi}{\mathrm{4}} \\ $$

Question Number 132031    Answers: 0   Comments: 3

Question Number 131932    Answers: 1   Comments: 0

if x=18 and y=17 then find (x+y)(x^2 +y^2 )(x^4 +y^4 )(x^8 +y^8 )

$${if}\:{x}=\mathrm{18}\:{and}\:{y}=\mathrm{17}\:{then}\:{find} \\ $$$$\left({x}+{y}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\left({x}^{\mathrm{4}} +{y}^{\mathrm{4}} \right)\left({x}^{\mathrm{8}} +{y}^{\mathrm{8}} \right) \\ $$

Question Number 131697    Answers: 2   Comments: 0

x^x =6 x=?

$${x}^{{x}} =\mathrm{6}\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$

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 =?

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

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