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AlgebraQuestion and Answers: Page 32

Question Number 210858    Answers: 2   Comments: 0

Solve The Equation: (7x+1)(9x+1)(21x+1)(63x+1)= ((160)/(189))

$$\mathrm{Solve}\:\mathrm{The}\:\mathrm{Equation}: \\ $$$$\left(\mathrm{7x}+\mathrm{1}\right)\left(\mathrm{9x}+\mathrm{1}\right)\left(\mathrm{21x}+\mathrm{1}\right)\left(\mathrm{63x}+\mathrm{1}\right)=\:\frac{\mathrm{160}}{\mathrm{189}} \\ $$

Question Number 210843    Answers: 1   Comments: 0

Question Number 210842    Answers: 1   Comments: 0

Question Number 210851    Answers: 1   Comments: 1

Question Number 210840    Answers: 1   Comments: 0

Prove that if x, y are rational numbers satisfying the equation x^5 + y^5 = 2(x^2)(y^2) then 1 - xy is the square of rational number

$$ \\ $$Prove that if x, y are rational numbers satisfying the equation x^5 + y^5 = 2(x^2)(y^2) then 1 - xy is the square of rational number

Question Number 210824    Answers: 0   Comments: 0

Question Number 210836    Answers: 0   Comments: 0

Question Number 210789    Answers: 1   Comments: 0

Question Number 210767    Answers: 2   Comments: 2

Question Number 210755    Answers: 0   Comments: 0

Question Number 210737    Answers: 1   Comments: 0

f(x)=(x^2 /(x^2 +1)) then f((1/1))+f((2/1))+.....+f(((100)/1))+f((1/2)) +f((2/2))+...+f(((100)/2))+f((1/(100)))+f((2/(100))) +......+f(((100)/(100)))=?

$${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:\:\:\:{then} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{1}}\right)+{f}\left(\frac{\mathrm{2}}{\mathrm{1}}\right)+.....+{f}\left(\frac{\mathrm{100}}{\mathrm{1}}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$+{f}\left(\frac{\mathrm{2}}{\mathrm{2}}\right)+...+{f}\left(\frac{\mathrm{100}}{\mathrm{2}}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{100}}\right)+{f}\left(\frac{\mathrm{2}}{\mathrm{100}}\right) \\ $$$$+......+{f}\left(\frac{\mathrm{100}}{\mathrm{100}}\right)=? \\ $$

Question Number 210728    Answers: 1   Comments: 0

Question Number 210718    Answers: 0   Comments: 1

If sin1° = a (1/(cos1°∙cos2°)) + (1/(cos2°∙cos3°)) +...+ (1/(cos44°∙cos45°)) = ?

$$\mathrm{If}\:\:\:\mathrm{sin1}°\:=\:\mathrm{a} \\ $$$$\frac{\mathrm{1}}{\mathrm{cos1}°\centerdot\mathrm{cos2}°}\:+\:\frac{\mathrm{1}}{\mathrm{cos2}°\centerdot\mathrm{cos3}°}\:+...+\:\frac{\mathrm{1}}{\mathrm{cos44}°\centerdot\mathrm{cos45}°}\:=\:? \\ $$

Question Number 210701    Answers: 1   Comments: 0

Question Number 210689    Answers: 1   Comments: 0

Question Number 210685    Answers: 3   Comments: 0

find ∫(1/x)dx

$${find} \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx} \\ $$

Question Number 210666    Answers: 1   Comments: 0

prove that p(n) is integer ∀ n∈Z p(n) = ((3n^7 +7n^3 +11n)/(21))

$$\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)\:\mathrm{is}\:\mathrm{integer}\:\forall\:\mathrm{n}\in\mathbb{Z} \\ $$$$\:\:\:\mathrm{p}\left(\mathrm{n}\right)\:=\:\frac{\mathrm{3n}^{\mathrm{7}} +\mathrm{7n}^{\mathrm{3}} +\mathrm{11n}}{\mathrm{21}} \\ $$

Question Number 210661    Answers: 0   Comments: 0

Question Number 210660    Answers: 0   Comments: 0

Question Number 210659    Answers: 0   Comments: 0

Question Number 210652    Answers: 0   Comments: 0

Question Number 210643    Answers: 3   Comments: 0

Question Number 210639    Answers: 3   Comments: 0

given that the roots of the equation 3x^2 −(4+2k)x+2k=0 are α and β find the value of k for which β=3α

$${given}\:{that}\:{the}\:{roots} \\ $$$$\:{of}\:{the}\:{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\left(\mathrm{4}+\mathrm{2}{k}\right){x}+\mathrm{2}{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$$${for}\:{which}\:\beta=\mathrm{3}\alpha \\ $$

Question Number 210630    Answers: 1   Comments: 0

Question Number 210629    Answers: 2   Comments: 0

Question Number 210679    Answers: 2   Comments: 0

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