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Question Number 150965 Answers: 1 Comments: 0

Question Number 150963 Answers: 1 Comments: 0

Given x ,y real number such that 0<(y/x)<(1/2). Find minimum value of ((2y)/(x−y)) +((3x)/(x+2y)) .

$${Given}\:{x}\:,{y}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:\mathrm{0}<\frac{{y}}{{x}}<\frac{\mathrm{1}}{\mathrm{2}}.\:{Find}\:{minimum}\:{value} \\ $$$${of}\:\frac{\mathrm{2}{y}}{{x}−{y}}\:+\frac{\mathrm{3}{x}}{{x}+\mathrm{2}{y}}\:.\: \\ $$

Question Number 150960 Answers: 1 Comments: 1

given x ,y is a prime number with x<y and x^3 +y^3 +20l8 =30y^2 −300y+30l8 find the value of x

$$\mathrm{given}\:\mathrm{x}\:,\mathrm{y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\: \\ $$$$\mathrm{with}\:\mathrm{x}<\mathrm{y}\:\mathrm{and}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{20l8}\:=\mathrm{30y}^{\mathrm{2}} −\mathrm{300y}+\mathrm{30l8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 150941 Answers: 2 Comments: 2

∫_1 ^4 ∣x−2∣dx please help me out

$$\int_{\mathrm{1}} ^{\mathrm{4}} \mid{x}−\mathrm{2}\mid{dx} \\ $$$${please}\:{help}\:{me}\:{out} \\ $$

Question Number 150932 Answers: 1 Comments: 0

I=∫((cosx − 2sinx)/(e^(2x) −sinx))dx=^?

$$\mathrm{I}=\int\frac{\mathrm{cosx}\:−\:\mathrm{2sinx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{sinx}}\mathrm{dx}\overset{?} {=} \\ $$

Question Number 150918 Answers: 2 Comments: 2

Question Number 150916 Answers: 1 Comments: 0

x^((x−1)^2 ) =2x+1 how can it solve this ?help me please

$${x}^{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } =\mathrm{2}{x}+\mathrm{1}\: \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve}\:{this}\:?{help}\:{me}\:{please} \\ $$

Question Number 150903 Answers: 1 Comments: 0

let x,y>0 , n∈N, show that (x+y)^n ≤2^(n−1) (x^n +y^n )..

$${let}\:{x},{y}>\mathrm{0}\:,\:{n}\in\mathbb{N}, \\ $$$${show}\:{that}\:\left({x}+{y}\right)^{{n}} \leqslant\mathrm{2}^{{n}−\mathrm{1}} \left({x}^{{n}} +{y}^{{n}} \right).. \\ $$

Question Number 150895 Answers: 1 Comments: 1

Question Number 150889 Answers: 1 Comments: 0

Question Number 150887 Answers: 1 Comments: 4

Question Number 150886 Answers: 0 Comments: 0

ϕ(n)=ϕ(n+1)=ϕ(n+2) n∈N n_(min) =? ϕ(n)− Euler funcsion

$$\:\varphi\left(\mathrm{n}\right)=\varphi\left(\mathrm{n}+\mathrm{1}\right)=\varphi\left(\mathrm{n}+\mathrm{2}\right)\:\:\mathrm{n}\in\mathrm{N}\:\mathrm{n}_{\mathrm{min}} =? \\ $$$$\varphi\left(\mathrm{n}\right)−\:\mathrm{Euler}\:\mathrm{funcsion} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 150885 Answers: 0 Comments: 0

Question Number 150884 Answers: 1 Comments: 0

Question Number 150883 Answers: 1 Comments: 0

prove that any real root 𝛂 of the equation: x^(6n) = 4x^(2n) + 4 ; n∈N-{0} verify: ∣𝛂∣ > (2)^(1/(2n))

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{real}\:\mathrm{root}\:\boldsymbol{\alpha}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}:\:\:\mathrm{x}^{\mathrm{6}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:+\:\mathrm{4}\:;\:\mathrm{n}\in\mathbb{N}-\left\{\mathrm{0}\right\} \\ $$$$\mathrm{verify}:\:\:\mid\boldsymbol{\alpha}\mid\:>\:\sqrt[{\mathrm{2}\boldsymbol{\mathrm{n}}}]{\mathrm{2}} \\ $$

Question Number 150881 Answers: 1 Comments: 0

y = ((a/b))^x ∙ ((b/x))^a ∙ ((x/a))^b ⇒ y^′ = ?

$$\mathrm{y}\:=\:\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{\boldsymbol{\mathrm{x}}} \centerdot\:\left(\frac{\mathrm{b}}{\mathrm{x}}\right)^{\boldsymbol{\mathrm{a}}} \centerdot\:\left(\frac{\mathrm{x}}{\mathrm{a}}\right)^{\boldsymbol{\mathrm{b}}} \:\Rightarrow\:\mathrm{y}\:^{'} \:=\:? \\ $$

Question Number 150880 Answers: 2 Comments: 0

if a;b;c>0 and a+b+c=1 find min((1/a) + (9/b) + ((25)/c)) = ? a)73 b)75 c)105 d)81 e)83

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{min}}\left(\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{9}}{\mathrm{b}}\:+\:\frac{\mathrm{25}}{\mathrm{c}}\right)\:=\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{7}\left.\mathrm{3}\left.\:\:\:\mathrm{b}\right)\mathrm{75}\:\:\:\mathrm{c}\right)\mathrm{105}\:\:\:\mathrm{d}\right)\mathrm{81}\:\:\:\mathrm{e}\right)\mathrm{83} \\ $$

Question Number 150876 Answers: 0 Comments: 0

Question Number 150865 Answers: 0 Comments: 0

Im{f'(z)} = 6x(2y-1) and f(0) = 3 - 2i, f(1) = 6 - 5i. Find f(2 + i)

Question Number 150864 Answers: 1 Comments: 0

Question Number 150862 Answers: 0 Comments: 0

Question Number 150861 Answers: 1 Comments: 0

Find the solution of : {_(x^2 +3xy+2y^2 −4 = 0) ^(2x^2 −2xy−3y^2 +7 = 0) Please show your working...

$${Find}\:\:{the}\:\:{solution}\:\:{of}\:\:: \\ $$$$\left\{_{{x}^{\mathrm{2}} +\mathrm{3}{xy}+\mathrm{2}{y}^{\mathrm{2}} −\mathrm{4}\:=\:\mathrm{0}} ^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{7}\:=\:\mathrm{0}} \right. \\ $$$${Please}\:\:{show}\:\:{your}\:\:{working}... \\ $$

Question Number 150859 Answers: 0 Comments: 0

Question Number 150853 Answers: 0 Comments: 2

log_(2021) (√(x : (√(x : (√(x :..)))))) = 674 find x=?

$$\mathrm{log}_{\mathrm{2021}} \:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::..}}}\:=\:\mathrm{674} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 150852 Answers: 0 Comments: 0

x;y;z>0 and x^2 +y^2 +z^2 =3 prove that xyz ≤ (((x + y + z - 1)/2))^2 ≤ 1

$$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{xyz}\:\leqslant\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:-\:\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{1} \\ $$

Question Number 150841 Answers: 2 Comments: 0

∫_( 0) ^( ∞) ((ln(1+a^2 x^2 ))/(1+b^2 x^2 )) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{b}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$

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