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Question Number 49126 Answers: 1 Comments: 1

prouve it existe 4 intergers a b c and d such n^2 −2 divise a^4 +b^4 +c^4 +d^4

$${prouve}\:{it}\:{existe}\:\mathrm{4}\:{intergers}\:{a}\:{b}\:{c}\:\:{and}\:\:{d}\:{such}\:{n}^{\mathrm{2}} −\mathrm{2}\:\:{divise}\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} \\ $$

Question Number 49123 Answers: 1 Comments: 1

If a^3 −a−1=0 then find the valueof a^4 +a^3 −a^2 −2a+1

$$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} −\mathrm{a}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{valueof} \\ $$$$\mathrm{a}^{\mathrm{4}} +\mathrm{a}^{\mathrm{3}} −\mathrm{a}^{\mathrm{2}} −\mathrm{2a}+\mathrm{1} \\ $$

Question Number 49121 Answers: 1 Comments: 0

Question Number 49118 Answers: 1 Comments: 0

Given that the equation 3x^2 +mx+n=0 has roots α + (1/β) and β + (1/(α )) find the value of m and n

$${Given}\:{that}\:{the}\:{equation}\:\:\mathrm{3}{x}^{\mathrm{2}} +{mx}+{n}=\mathrm{0}\:{has}\:{roots}\:\alpha\:+\:\frac{\mathrm{1}}{\beta}\:{and} \\ $$$$\beta\:+\:\frac{\mathrm{1}}{\alpha\:}\:{find}\:{the}\:{value}\:{of}\:\:{m}\:{and}\:{n} \\ $$$$ \\ $$

Question Number 49116 Answers: 1 Comments: 2

Give a proof for : 2 = (√(2 + (√(2 + (√( 2 + (√(2 + (√( 2 ... ))))))))))

$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{for}\:: \\ $$$$\mathrm{2}\:=\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:...\:}}}}} \\ $$

Question Number 49112 Answers: 0 Comments: 1

Question Number 49111 Answers: 1 Comments: 0

Question Number 49101 Answers: 0 Comments: 0

Question Number 49100 Answers: 0 Comments: 0

Question Number 49099 Answers: 0 Comments: 0

Question Number 49097 Answers: 1 Comments: 0

Question Number 49096 Answers: 1 Comments: 0

Question Number 49095 Answers: 1 Comments: 0

prove the existence of n integrs naturals x_1 ,x_2 ,....x_n with x_i ≠x_j for i≠j and (1/x_1 ) +(1/x_2 ) +....+(1/x_n ) =1 .

$${prove}\:{the}\:{existence}\:{of}\:{n}\:{integrs}\:{naturals}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,....{x}_{{n}} \:\:\:\:{with}\:{x}_{{i}} \neq{x}_{{j}} {for}\:{i}\neq{j} \\ $$$${and}\:\frac{\mathrm{1}}{{x}_{\mathrm{1}} }\:+\frac{\mathrm{1}}{{x}_{\mathrm{2}} }\:+....+\frac{\mathrm{1}}{{x}_{{n}} }\:=\mathrm{1}\:. \\ $$

Question Number 49094 Answers: 0 Comments: 1

calculate ∫_(−π) ^π (x^2 /(sin(sinx)+(√(1+sin^2 (sinx)))))dx

$${calculate}\:\int_{−\pi} ^{\pi} \:\:\frac{{x}^{\mathrm{2}} }{{sin}\left({sinx}\right)+\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} \left({sinx}\right)}}{dx} \\ $$

Question Number 49093 Answers: 2 Comments: 0

Question Number 49092 Answers: 0 Comments: 0

Question Number 49090 Answers: 0 Comments: 1

How do you create a new math page without erasing the current page ...

$${How}\:{do}\:{you}\:{create}\:{a}\:{new}\:{math}\:{page}\:{without}\:{erasing}\:{the}\:{current}\:{page}\:... \\ $$

Question Number 49083 Answers: 0 Comments: 0

Question Number 49078 Answers: 1 Comments: 0

Question Number 49077 Answers: 0 Comments: 0

Question Number 49064 Answers: 1 Comments: 0

solve for 0°≤θ≤2π the equation cos(θ + (π/3)) = (1/2)

$${solve}\:{for}\:\mathrm{0}°\leqslant\theta\leqslant\mathrm{2}\pi\:{the}\:{equation} \\ $$$${cos}\left(\theta\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 49061 Answers: 2 Comments: 0

The numerical value of tan (2 tan^(−1) (1/5) − (π/4)) is

$$\mathrm{The}\:\mathrm{numerical}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mathrm{tan}\:\left(\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{5}}\:−\:\frac{\pi}{\mathrm{4}}\right)\:\:\mathrm{is} \\ $$

Question Number 49060 Answers: 2 Comments: 0

Question Number 49037 Answers: 0 Comments: 0

Question Number 49036 Answers: 1 Comments: 4

Question Number 49035 Answers: 0 Comments: 0

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