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Question Number 172021    Answers: 1   Comments: 0

solve: 2^x^2 =x^(2x)

$${solve}: \\ $$$$\mathrm{2}^{{x}^{\mathrm{2}} } ={x}^{\mathrm{2}{x}} \\ $$

Question Number 172024    Answers: 1   Comments: 0

let α and β be the root of the equation ax^2 +bx+c=0. find the equation whose roots are ((1/α)+(1/β)) and ((1/α)−(1/β))

$${let}\:\alpha\:{and}\:\beta\:{be}\:{the}\:{root}\:{of}\:{the}\:{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}.\:{find}\:{the}\:{equation}\:{whose}\:{roots} \\ $$$${are}\:\left(\frac{\mathrm{1}}{\alpha}+\frac{\mathrm{1}}{\beta}\right)\:{and}\:\left(\frac{\mathrm{1}}{\alpha}−\frac{\mathrm{1}}{\beta}\right) \\ $$

Question Number 172002    Answers: 0   Comments: 0

if y=bcoslog((x/n))^n , then (dy/dx)=?

$${if}\:{y}={bcoslog}\left(\frac{{x}}{{n}}\right)^{{n}} ,\:{then} \\ $$$$\frac{{dy}}{{dx}}=? \\ $$

Question Number 172001    Answers: 0   Comments: 0

solve: ∫(((√(x^2 +1)) −(√(x^2 −1)))/( (√(x^4 −1))))dx

$${solve}: \\ $$$$\int\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}}{dx} \\ $$

Question Number 172000    Answers: 0   Comments: 0

prove that: ((sinx)/(sin3x))+((tanx)/(tan3x))=1

$${prove}\:{that}: \\ $$$$\frac{{sinx}}{{sin}\mathrm{3}{x}}+\frac{{tanx}}{{tan}\mathrm{3}{x}}=\mathrm{1} \\ $$

Question Number 171999    Answers: 1   Comments: 0

resolve: ((4(x−4))/(x^2 −2x−3)) into partial fraction

$${resolve}: \\ $$$$\frac{\mathrm{4}\left({x}−\mathrm{4}\right)}{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}\:{into}\:{partial}\:{fraction} \\ $$

Question Number 171998    Answers: 0   Comments: 0

if x^3 +(1/x^3 )=81, then find ((x^6 +1)/(x^5 +5x))

$${if} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{81},\:{then}\:{find}\: \\ $$$$\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{5}{x}} \\ $$

Question Number 172019    Answers: 0   Comments: 0

solve: x^3 +9x^2 y=10 y^3 +xy^2 =2

$${solve}: \\ $$$${x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} {y}=\mathrm{10} \\ $$$${y}^{\mathrm{3}} +{xy}^{\mathrm{2}} =\mathrm{2} \\ $$

Question Number 172025    Answers: 1   Comments: 0

find the root of x^4 +4x^3 +11x^2 +14x−30=0.

$${find}\:{the}\:{root}\:{of}\: \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{11}{x}^{\mathrm{2}} +\mathrm{14}{x}−\mathrm{30}=\mathrm{0}. \\ $$

Question Number 171995    Answers: 0   Comments: 0

solve: ((x/(12)))^(log_(√3) x) =((x/(18)))^(log_(√2) x)

$${solve}: \\ $$$$\left(\frac{{x}}{\mathrm{12}}\right)^{{log}_{\sqrt{\mathrm{3}}} \:{x}} =\left(\frac{{x}}{\mathrm{18}}\right)^{{log}_{\sqrt{\mathrm{2}}} {x}} \\ $$$$ \\ $$

Question Number 171993    Answers: 0   Comments: 3

Question Number 172020    Answers: 1   Comments: 0

solve: 2^x =10x

$${solve}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{10}{x} \\ $$

Question Number 171990    Answers: 1   Comments: 0

solve: log_7 2 + log_(49) x =log_7 (√3)

$${solve}: \\ $$$${log}_{\mathrm{7}} \mathrm{2}\:+\:{log}_{\mathrm{49}} {x}\:={log}_{\mathrm{7}} \sqrt{\mathrm{3}} \\ $$

Question Number 171989    Answers: 1   Comments: 0

solve: A two digit number is such that 4 times the unit digit is 5 more than thrice the ten digit. when the digit are reversed the number is increase by nine, find the number

$${solve}:\:{A}\:{two}\:{digit}\:{number}\:{is}\:{such} \\ $$$${that}\:\mathrm{4}\:{times}\:{the}\:{unit}\:{digit}\:{is}\:\mathrm{5}\:{more}\: \\ $$$${than}\:{thrice}\:{the}\:{ten}\:{digit}.\:{when}\:{the} \\ $$$${digit}\:{are}\:{reversed}\:{the}\:{number}\:{is}\: \\ $$$${increase}\:{by}\:{nine},\:{find}\:{the}\:{number} \\ $$$$ \\ $$

Question Number 171988    Answers: 0   Comments: 0

solve: x^2 =16^x

$${solve}: \\ $$$${x}^{\mathrm{2}} =\mathrm{16}^{{x}} \\ $$

Question Number 171984    Answers: 0   Comments: 0

Question Number 171979    Answers: 1   Comments: 0

Question Number 171972    Answers: 1   Comments: 0

Question Number 171971    Answers: 2   Comments: 0

∫(x/(x^2 +4x+3)) dx=...

$$\int\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}\:{dx}=... \\ $$

Question Number 171966    Answers: 0   Comments: 0

Question Number 171955    Answers: 2   Comments: 0

f(x)+ f((1/(1−x))) = 1+(1/(x(1−x))) f(x) = ??

$$\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\:\boldsymbol{{f}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)} \\ $$$$\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\:??\:\:\:\:\:\:\:\:\: \\ $$

Question Number 171954    Answers: 0   Comments: 0

Find without softs: ∫_(1/e) ^( e) (dx/((1 + x^2 )(1 + x log^7 x)))

$$\mathrm{Find}\:\mathrm{without}\:\mathrm{softs}: \\ $$$$\int_{\frac{\mathrm{1}}{\boldsymbol{\mathrm{e}}}} ^{\:\boldsymbol{\mathrm{e}}} \:\frac{\mathrm{dx}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:\mathrm{x}\:\mathrm{log}^{\mathrm{7}} \:\mathrm{x}\right)} \\ $$

Question Number 171985    Answers: 0   Comments: 0

In △ABC , O-circumcentr , G-centroid. Prove that: OG∥BC⇔(b^2 −c^2 )^2 =4a^2 (9R^2 −a^2 −b^2 −c^2 )

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{O}-\mathrm{circumcentr}\:,\:\mathrm{G}-\mathrm{centroid}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{OG}\parallel\mathrm{BC}\Leftrightarrow\left(\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{4a}^{\mathrm{2}} \left(\mathrm{9R}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right) \\ $$

Question Number 171944    Answers: 0   Comments: 5

if a+b+c=2196 (a)^(1/3) +b+c=2076 a+(b)^(1/3) +c=1860 a+b+(c)^(1/3) =480, determine the value of a^(2/3) +b^(2/3) +c^(2/3) , if a,b,c are all integer.

$${if} \\ $$$${a}+{b}+{c}=\mathrm{2196} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+{b}+{c}=\mathrm{2076} \\ $$$${a}+\sqrt[{\mathrm{3}}]{{b}}\:+{c}=\mathrm{1860} \\ $$$${a}+{b}+\sqrt[{\mathrm{3}}]{{c}}\:=\mathrm{480},\:{determine}\:{the}\:{value}\:{of} \\ $$$${a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}} +{c}^{\frac{\mathrm{2}}{\mathrm{3}}} ,\:{if}\:{a},{b},{c}\:{are}\:{all}\:{integer}. \\ $$

Question Number 171941    Answers: 0   Comments: 3

(√a)+(√b)=(√(2009)). find a and b.

$$\sqrt{{a}}+\sqrt{{b}}=\sqrt{\mathrm{2009}}.\:{find}\:{a}\:{and}\:{b}. \\ $$

Question Number 171930    Answers: 0   Comments: 0

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