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Question Number 151344 Answers: 2 Comments: 0

x^2 - 4x + 1 = 0 ⇒ x^3 + (1/x^3 ) = ?

$$\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{4x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 151341 Answers: 1 Comments: 0

∫_α ^β (dx/(x(√((x−α)(β−x) ))))=(π/( (√(αβ)))) where α,β >0

$$\int_{\alpha} ^{\beta} \frac{\mathrm{dx}}{\mathrm{x}\sqrt{\left(\mathrm{x}−\alpha\right)\left(\beta−\mathrm{x}\right)\:}}=\frac{\pi}{\:\sqrt{\alpha\beta}} \\ $$$$\mathrm{where}\:\alpha,\beta\:>\mathrm{0} \\ $$

Question Number 151340 Answers: 1 Comments: 0

Evaluate ∫_(−1) ^1 (((2x^(332) +x^(998) +4x^(1668) .sin x^(691) ))/(1+x^(666) ))dx

$$\mathrm{Evaluate} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\left(\mathrm{2x}^{\mathrm{332}} +\mathrm{x}^{\mathrm{998}} +\mathrm{4x}^{\mathrm{1668}} .\mathrm{sin}\:\mathrm{x}^{\mathrm{691}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{666}} }\mathrm{dx} \\ $$

Question Number 151332 Answers: 1 Comments: 2

which is larger? 2^(√(10)) or 3^2

$$\mathrm{which}\:\mathrm{is}\:\mathrm{larger}? \\ $$$$\mathrm{2}^{\sqrt{\mathrm{10}}} \:\:\mathrm{or}\:\:\mathrm{3}^{\mathrm{2}} \\ $$

Question Number 151322 Answers: 1 Comments: 1

Determine all pairs (x;y) of integers which satisfy: x^3 - 3x + y = 0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\:\left(\mathrm{x};\mathrm{y}\right)\:\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{which}\:\mathrm{satisfy}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{3x}\:+\:\mathrm{y}\:=\:\mathrm{0} \\ $$

Question Number 151321 Answers: 0 Comments: 0

Question Number 151317 Answers: 2 Comments: 0

if x=(((√7) - (√6)))^(1/3) + (((√7) + (√6)))^(1/3) find E(x) = x^6 - 6x^4 + 9x^2 = ?

$$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}=\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:-\:\sqrt{\mathrm{6}}}\:+\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:+\:\sqrt{\mathrm{6}}} \\ $$$$\mathrm{find}\:\:\mathrm{E}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{6x}^{\mathrm{4}} \:+\:\mathrm{9x}^{\mathrm{2}} \:=\:? \\ $$

Question Number 151316 Answers: 1 Comments: 0

Find positive integers a and b such that ((a)^(1/3) +(b)^(1/3) −1)^2 = 49+ 20(6)^(1/3)

$$\:\:\:\:\:\:{Find}\:{positive}\:{integers}\: \\ $$$$\:\:\:\:\:{a}\:{and}\:{b}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\left(\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:−\mathrm{1}\right)^{\mathrm{2}} =\:\mathrm{49}+\:\mathrm{20}\sqrt[{\mathrm{3}}]{\mathrm{6}}\: \\ $$

Question Number 151315 Answers: 1 Comments: 0

if x^2 +y^2 =16^2 ; y^2 +z^2 =24^2 z^2 +t^2 =42^2 and t^2 +x^2 =38^2 find max[(x+z)(y+t)]=?

$$\mathrm{if}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{16}^{\mathrm{2}} \:\:;\:\:\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{24}^{\mathrm{2}} \\ $$$$\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} =\mathrm{42}^{\mathrm{2}} \:\:\mathrm{and}\:\:\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} =\mathrm{38}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\:\mathrm{max}\left[\left(\mathrm{x}+\mathrm{z}\right)\left(\mathrm{y}+\mathrm{t}\right)\right]=? \\ $$

Question Number 151311 Answers: 0 Comments: 0

Question Number 151308 Answers: 0 Comments: 0

Question Number 151307 Answers: 2 Comments: 0

if x(√x) - 26(√x) = 5 find x - 5(√x) = ?

$$\mathrm{if}\:\:\mathrm{x}\sqrt{\mathrm{x}}\:-\:\mathrm{26}\sqrt{\mathrm{x}}\:=\:\mathrm{5} \\ $$$$\mathrm{find}\:\:\mathrm{x}\:-\:\mathrm{5}\sqrt{\mathrm{x}}\:=\:? \\ $$

Question Number 151300 Answers: 3 Comments: 0

5 ∙ 6,02∙10^(23) = ? (solution) a)3,01∙10^(24) b)3,01∙10^(22)

$$\mathrm{5}\:\centerdot\:\mathrm{6},\mathrm{02}\centerdot\mathrm{10}^{\mathrm{23}} \:=\:?\:\left(\mathrm{solution}\right) \\ $$$$\left.\mathrm{a}\left.\right)\mathrm{3},\mathrm{01}\centerdot\mathrm{10}^{\mathrm{24}} \:\:\:\mathrm{b}\right)\mathrm{3},\mathrm{01}\centerdot\mathrm{10}^{\mathrm{22}} \\ $$

Question Number 151294 Answers: 1 Comments: 0

Question Number 151287 Answers: 0 Comments: 2

I = ∫_(x=a) ^( x=b) (√(u^2 + v^2 x^2 − 2uvwx)) dx = ?

$${I}\:=\:\int_{{x}={a}} ^{\:{x}={b}} \sqrt{{u}^{\mathrm{2}} \:+\:{v}^{\mathrm{2}} {x}^{\mathrm{2}} \:−\:\mathrm{2}{uvwx}}\:{dx}\:=\:? \\ $$

Question Number 151284 Answers: 1 Comments: 0

if (a/3^(x-1) ) = (b/3^(y+2) ) = (c/3^(z-1) ) = (1/5) find abc = ?

$$\mathrm{if}\:\:\frac{\mathrm{a}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}-\mathrm{1}} }\:=\:\frac{\mathrm{b}}{\mathrm{3}^{\boldsymbol{\mathrm{y}}+\mathrm{2}} }\:=\:\frac{\mathrm{c}}{\mathrm{3}^{\boldsymbol{\mathrm{z}}-\mathrm{1}} }\:=\:\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\mathrm{abc}\:=\:? \\ $$

Question Number 151282 Answers: 0 Comments: 0

Question Number 151281 Answers: 0 Comments: 0

Question Number 151278 Answers: 1 Comments: 0

∫ (e^(√(x - 1)) /( (√(x - 1)))) dx = ?

$$\int\:\frac{\boldsymbol{\mathrm{e}}^{\sqrt{\boldsymbol{\mathrm{x}}\:-\:\mathrm{1}}} }{\:\sqrt{\boldsymbol{\mathrm{x}}\:-\:\mathrm{1}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 151276 Answers: 2 Comments: 2

∫_0 ^(2π) cos^(−1) (cos x)dx

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{cos}^{−\mathrm{1}} \left(\mathrm{cos}\:\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 151272 Answers: 0 Comments: 1

Question Number 151269 Answers: 0 Comments: 1

Question Number 151268 Answers: 0 Comments: 0

Σ_(r=1) ^∞ (((−1)^(r−1) )/r)[ψ((r/2)+(1/4))−ψ((r/2)−(1/4))]

$$\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} }{{r}}\left[\psi\left(\frac{{r}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}\right)−\psi\left(\frac{{r}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}\right)\right] \\ $$

Question Number 151265 Answers: 1 Comments: 3

Question Number 151256 Answers: 2 Comments: 0

A_n =2^n +3^n +4^n +5^n B_n =100^n +101^n +102^n +103^n 1)find values of n while 7∣A_n 2) show that B_n ≡A_n [7 ]

$$\:{A}_{{n}} =\mathrm{2}^{{n}} +\mathrm{3}^{{n}} +\mathrm{4}^{{n}} +\mathrm{5}^{{n}} \\ $$$${B}_{{n}} =\mathrm{100}^{{n}} +\mathrm{101}^{{n}} +\mathrm{102}^{{n}} +\mathrm{103}^{{n}} \\ $$$$\left.\mathrm{1}\right)\boldsymbol{{find}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{n}}\:\boldsymbol{{while}}\:\mathrm{7}\mid\boldsymbol{{A}}_{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{B}}_{\boldsymbol{{n}}} \equiv\boldsymbol{{A}}_{\boldsymbol{{n}}} \left[\mathrm{7}\:\right] \\ $$

Question Number 151248 Answers: 1 Comments: 0

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