Question and Answers Forum

AllQuestion and Answers: Page 1405

Question Number 64202 Answers: 0 Comments: 0

Prove 385^(1980) +18^(1980) is not a square.

$$\mathrm{Prove}\:\mathrm{385}^{\mathrm{1980}} +\mathrm{18}^{\mathrm{1980}} \:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{square}.\: \\ $$

Question Number 64201 Answers: 2 Comments: 0

Find all positive solutions x+y+z = 1 x^3 +y^3 + z^3 + xyz = x^4 + y^4 + z^4 +1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{solutions}\: \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{xyz}\:=\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:+\mathrm{1} \\ $$

Question Number 64200 Answers: 1 Comments: 1

Question Number 64187 Answers: 1 Comments: 0

Question Number 64186 Answers: 1 Comments: 0

Question Number 64185 Answers: 2 Comments: 3

Question Number 64176 Answers: 1 Comments: 0

Question Number 64175 Answers: 0 Comments: 1

m^3 −4m

$${m}^{\mathrm{3}} \:−\mathrm{4}{m}\: \\ $$

Question Number 64174 Answers: 0 Comments: 0

2^n / 5^2^n + 1 infinite series sum ffom 0 to infinity

$$\mathrm{2}^{{n}} \:/\:\mathrm{5}^{\mathrm{2}^{{n}} } \:+\:\mathrm{1}\:{infinite}\:{series}\:{sum}\:{ffom}\:\mathrm{0}\:{to}\: \\ $$$${infinity} \\ $$

Question Number 64173 Answers: 0 Comments: 1

show tbat Π_(k=1) ^n (1−((sin^2 ((θ/(2n))))/(sin^2 (((2k−1)/4)π))))=cos(θ)

$${show}\:{tbat}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}−\frac{{sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}{n}}\right)}{{sin}^{\mathrm{2}} \left(\frac{\mathrm{2}{k}−\mathrm{1}}{\mathrm{4}}\pi\right)}\right)={cos}\left(\theta\right) \\ $$

Question Number 64166 Answers: 1 Comments: 0

calculate A_n =∫_(−∞) ^(+∞) (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) with n integr natural and n≥1

$${calculate}\:\:{A}_{{n}} =\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$$${with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 64160 Answers: 2 Comments: 5

let f(x) =∫_0 ^1 (dt/(x +2^t )) with x>0 1) determine a explicit form for f(x) 2) determine also g(x)=∫_0 ^1 (dt/((x+2^x )^2 )) 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^1 (dt/(1+2^t )) and ∫_0 ^1 (dt/((1+2^t )^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{{x}\:+\mathrm{2}^{{t}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left({x}+\mathrm{2}^{{x}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral}\: \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{2}^{{t}} }\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+\mathrm{2}^{{t}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 64159 Answers: 1 Comments: 1

calculate ∫_0 ^1 (dx/(3+2^x ))

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\mathrm{3}+\mathrm{2}^{{x}} } \\ $$

Question Number 64158 Answers: 0 Comments: 0

Question Number 64153 Answers: 1 Comments: 0

solve to z^2 x^2 −y^2 =24

$${solve}\:{to}\:{z}^{\mathrm{2}} \:\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{24} \\ $$

Question Number 64150 Answers: 1 Comments: 2

calculate ∫_(−∞) ^(+∞) (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)} \\ $$

Question Number 64147 Answers: 2 Comments: 0

Question Number 64139 Answers: 1 Comments: 2

∫_( 0) ^1 (dx/(x^2 +2x cos α+1)) = α sin α

$$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:\mathrm{cos}\:\alpha+\mathrm{1}}\:=\:\alpha\:\mathrm{sin}\:\alpha \\ $$

Question Number 64138 Answers: 1 Comments: 0

Question Number 64130 Answers: 2 Comments: 1

(√(4x+((12)/x)))=((x^2 +7)/(x+1)) x=?

$$\sqrt{\mathrm{4}\boldsymbol{\mathrm{x}}+\frac{\mathrm{12}}{\boldsymbol{\mathrm{x}}}}=\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{7}}{\boldsymbol{\mathrm{x}}+\mathrm{1}} \\ $$$$\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 64129 Answers: 0 Comments: 0

Question Number 64126 Answers: 1 Comments: 0

Question Number 64124 Answers: 0 Comments: 0

(√(2014))x^3 −4029x^2 +2=0 x_1 <x_2 <x_3 x_2 (x_1 +x_3 )=?

$$\sqrt{\mathrm{2014}}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{4029}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} <\boldsymbol{\mathrm{x}}_{\mathrm{2}} <\boldsymbol{\mathrm{x}}_{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}_{\mathrm{1}} +\boldsymbol{\mathrm{x}}_{\mathrm{3}} \right)=? \\ $$

Question Number 64122 Answers: 0 Comments: 0

∫tan(1/x)dx

$$\int{tan}\left(\mathrm{1}/{x}\right){dx} \\ $$

Question Number 64121 Answers: 0 Comments: 0

∫tan(1/x)dx

$$\int{tan}\left(\mathrm{1}/{x}\right){dx} \\ $$

Question Number 64119 Answers: 3 Comments: 1

Pg 1400 Pg 1401 Pg 1402 Pg 1403 Pg 1404 Pg 1405 Pg 1406 Pg 1407 Pg 1408 Pg 1409

Contact: info@tinkutara.com