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Question Number 195872 Answers: 1 Comments: 0

z_1 , z_2 , z_3 ∈C.∣z_1 ∣=∣z_2 ∣=∣z_3 ∣=1. Prove that (((z_1 +z_2 )(z_2 +z_3 )(z_3 +z_1 ))/(z_1 z_2 z_3 ))∈R.

$${z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \in\mathbb{C}.\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)\left({z}_{\mathrm{2}} +{z}_{\mathrm{3}} \right)\left({z}_{\mathrm{3}} +{z}_{\mathrm{1}} \right)}{{z}_{\mathrm{1}} {z}_{\mathrm{2}} {z}_{\mathrm{3}} }\in\mathbb{R}. \\ $$

Question Number 195870 Answers: 1 Comments: 4

Question Number 195860 Answers: 0 Comments: 0

Question Number 195855 Answers: 1 Comments: 0

{ ((3(√(((12))^(1/3) −(3)^(1/3) ))=(x)^(1/3) +(y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? please help me

$$\begin{cases}{\mathrm{3}\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{12}}−\sqrt[{\mathrm{3}}]{\mathrm{3}}}=\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}−\sqrt[{\mathrm{3}}]{{z}}}\\{{x},{y},{z}\:\in\:{N}}\end{cases}\:\:\Rightarrow\:{x},{y},{z}\:=? \\ $$$${please}\:{help}\:{me} \\ $$

Question Number 195854 Answers: 3 Comments: 2

Question Number 195848 Answers: 2 Comments: 0

Please how did ∣z−a∣=r became z= a + re^(iθ) ?

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{did}\:\mid\mathrm{z}−\mathrm{a}\mid=\mathrm{r}\:\mathrm{became}\: \\ $$$$\mathrm{z}=\:\mathrm{a}\:+\:\mathrm{re}^{\mathrm{i}\theta} ? \\ $$

Question Number 195846 Answers: 1 Comments: 0

{ (( Ω_1 = ∫_0 ^( (π/2)) (( x^( 2) )/(sin^( 2) (x))) dx )),(( ⇒ (Ω_1 /Ω_( 2) ) = ? )),(( Ω_( 2) = ∫_0 ^( (π/2)) (x/(tan(x))) dx)) :}

$$ \\ $$$$\:\:\:\:\:\:\begin{cases}{\:\:\:\Omega_{\mathrm{1}} \:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{x}^{\:\mathrm{2}} }{{sin}^{\:\mathrm{2}} \left({x}\right)}\:{dx}\:}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\frac{\Omega_{\mathrm{1}} }{\Omega_{\:\mathrm{2}} }\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\Omega_{\:\mathrm{2}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}\:{dx}}\end{cases} \\ $$$$ \\ $$

Question Number 195840 Answers: 0 Comments: 4

find the valur lim_(→0) ((x−sinx)/x^3 )

$${find}\:{the}\:{valur} \\ $$$$\:\:{li}\underset{\rightarrow\mathrm{0}} {{m}}\:\frac{{x}−{sinx}}{{x}^{\mathrm{3}} } \\ $$

Question Number 195838 Answers: 1 Comments: 0

Question Number 195833 Answers: 1 Comments: 1

how does the d get max

$${how}\:{does}\:\:{the}\:{d}\:{get}\:{max} \\ $$

Question Number 195823 Answers: 1 Comments: 0

Question Number 195820 Answers: 1 Comments: 0

a,b,c>0 &abc=1,prove that (1/(1+a+b))+(1/(1+b+c))+(1/(1+c+a))≤1

$${a},{b},{c}>\mathrm{0}\:\&{abc}=\mathrm{1},{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{a}+{b}}+\frac{\mathrm{1}}{\mathrm{1}+{b}+{c}}+\frac{\mathrm{1}}{\mathrm{1}+{c}+{a}}\leqslant\mathrm{1} \\ $$

Question Number 195815 Answers: 0 Comments: 0

Question Number 195814 Answers: 1 Comments: 0

Question Number 195813 Answers: 0 Comments: 0

{ ((3(√(((12))^(1/3) −(3)^(1/3) )) = (x)^(1/3) + (y)^(1/3) −(z)^(1/3) )),((x,y,z ∈ N)) :} ⇒ x,y,z =? mr.W please help me and other my friends please help me

$$\begin{cases}{\mathrm{3}\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{12}}−\sqrt[{\mathrm{3}}]{\mathrm{3}}}\:\:=\:\sqrt[{\mathrm{3}}]{{x}}\:+\:\sqrt[{\mathrm{3}}]{{y}}\:−\sqrt[{\mathrm{3}}]{{z}}}\\{{x},{y},{z}\:\in\:{N}}\end{cases}\:\Rightarrow\:{x},{y},{z}\:=? \\ $$$${mr}.{W}\:{please}\:{help}\:{me} \\ $$$${and}\:{other}\:{my}\:{friends}\:{please}\:{help}\:{me} \\ $$

Question Number 195809 Answers: 2 Comments: 3

if x^5 +x+1=0, find x^3 −x^2 =?

$${if}\:{x}^{\mathrm{5}} +{x}+\mathrm{1}=\mathrm{0},\:{find}\:{x}^{\mathrm{3}} −{x}^{\mathrm{2}} =? \\ $$

Question Number 195806 Answers: 1 Comments: 0

Question Number 195802 Answers: 0 Comments: 0

Question Number 195803 Answers: 0 Comments: 0

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

$$\int\frac{\sqrt{{x}}{dx}}{\:\sqrt{−\mathrm{1}+\sqrt{\mathrm{2}−\left({x}+\mathrm{1}\right)^{\mathrm{2}} }}} \\ $$

Question Number 195799 Answers: 2 Comments: 0

Question Number 195797 Answers: 0 Comments: 0

Question Number 195790 Answers: 1 Comments: 2

a,b,c are positive real numbers and abc =1 prove that (a−1+(1/b))(b−1+(1/c))(c−1+(1/a))≤1

$${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers}\:{and}\:{abc}\:=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left({a}−\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left({b}−\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\left({c}−\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\leqslant\mathrm{1} \\ $$

Question Number 195765 Answers: 2 Comments: 0

hello { ((x^3 +(1/x^3 ) = 18)),((x>1)) :} ⇒ x^5 −(1/x^5 ) = ?

$${hello} \\ $$$$ \\ $$$$\:\begin{cases}{{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:=\:\mathrm{18}}\\{{x}>\mathrm{1}}\end{cases}\:\:\Rightarrow\:\:\:{x}^{\mathrm{5}} −\frac{\mathrm{1}}{{x}^{\mathrm{5}} }\:=\:? \\ $$

Question Number 195755 Answers: 1 Comments: 0

Question Number 195753 Answers: 1 Comments: 0

Calculer ∫^( 1) _( 0) ((ln^2 t)/( (√(1−t^2 ))))dt

$$\mathrm{Calculer}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} {t}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{dt} \\ $$

Question Number 195751 Answers: 0 Comments: 0

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