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AlgebraQuestion and Answers: Page 29

Question Number 210895 Answers: 4 Comments: 0

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Question Number 210871 Answers: 0 Comments: 1

7(x−2)((√(10 + x)) − ((7−x))^(1/3) )−15x + 6 = 0 x = ?

$$\mathrm{7}\left(\mathrm{x}−\mathrm{2}\right)\left(\sqrt{\mathrm{10}\:+\:\mathrm{x}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{x}}\right)−\mathrm{15x}\:+\:\mathrm{6}\:=\:\mathrm{0} \\ $$$$\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 210870 Answers: 0 Comments: 1

8x^2 − 13x + 11 = (2/x) + (1 + (3/x)) ((3x^2 −2))^(1/3) x = ?

$$\mathrm{8x}^{\mathrm{2}} \:−\:\mathrm{13x}\:+\:\mathrm{11}\:=\:\frac{\mathrm{2}}{\mathrm{x}}\:+\:\left(\mathrm{1}\:+\:\frac{\mathrm{3}}{\mathrm{x}}\right)\:\sqrt[{\mathrm{3}}]{\mathrm{3x}^{\mathrm{2}} −\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 210868 Answers: 1 Comments: 5

let p ,q be reals such that p>q>0 define the sequence {x_n } where x_1 = p+q and x_n = x_1 −((pq)/x_(n−1) ) for n≥2 for all n then x_n = ??

$$\mathrm{let}\:\mathrm{p}\:,\mathrm{q}\:\mathrm{be}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that}\:\mathrm{p}>\mathrm{q}>\mathrm{0}\:\mathrm{define} \\ $$$$\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{x}_{\mathrm{n}} \right\}\:\mathrm{where}\:\mathrm{x}_{\mathrm{1}} =\:\mathrm{p}+\mathrm{q}\:\mathrm{and} \\ $$$$\mathrm{x}_{\mathrm{n}} \:=\:\mathrm{x}_{\mathrm{1}} −\frac{\mathrm{pq}}{\mathrm{x}_{\mathrm{n}−\mathrm{1}} }\:\mathrm{for}\:\mathrm{n}\geqslant\mathrm{2}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:\mathrm{then}\:\mathrm{x}_{\mathrm{n}} \:=\:?? \\ $$

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

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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)))=?

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))

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

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