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The real roots of the equation x^2 +6x+c=0 differ by 2n, where n is a real non−zero. Show that n^2 =9−c Given that the roots also have opposite signs, find the set of possible values of n

$$\mathrm{The}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{differ}\:\mathrm{by}\:\mathrm{2n},\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{non}−\mathrm{zero}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{n}^{\mathrm{2}} =\mathrm{9}−\mathrm{c} \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{also}\:\mathrm{have}\:\mathrm{opposite} \\ $$$$\mathrm{signs},\:\mathrm{find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n} \\ $$

Question Number 207576 Answers: 1 Comments: 2

Question Number 207543 Answers: 2 Comments: 1

Question Number 207565 Answers: 2 Comments: 0

find ∫_0 ^(π/2) (x^2 /(tan^2 x))dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{{tan}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 207533 Answers: 2 Comments: 1

Question Number 207528 Answers: 2 Comments: 0

Question Number 207519 Answers: 1 Comments: 0

Find: lim_(x→2^− ) (((x + 2)∙(x + 1))/(∣x + 2∣)) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$

Question Number 207518 Answers: 1 Comments: 0

cosx cos3x = cos5x cos7x ⇒ x = ?

$$\mathrm{cos}\boldsymbol{\mathrm{x}}\:\mathrm{cos3}\boldsymbol{\mathrm{x}}\:\:=\:\:\mathrm{cos5}\boldsymbol{\mathrm{x}}\:\mathrm{cos7}\boldsymbol{\mathrm{x}} \\ $$$$\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207516 Answers: 2 Comments: 1

3(sinθ − cosθ)^4 + 6(sinθ + cosθ)^2 + 4(sin^6 θ + cos^6 θ) = ?

$$\mathrm{3}\left(\mathrm{sin}\theta\:−\:\mathrm{cos}\theta\right)^{\mathrm{4}} \:+\:\mathrm{6}\left(\mathrm{sin}\theta\:+\:\mathrm{cos}\theta\right)^{\mathrm{2}} \\ $$$$+\:\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} \theta\:+\:\mathrm{cos}^{\mathrm{6}} \theta\right)\:=\:? \\ $$

Question Number 207509 Answers: 1 Comments: 0

Question Number 207502 Answers: 2 Comments: 0

(6/(∣x − 4∣ − 3)) ≥ 1

$$\frac{\mathrm{6}}{\mid\boldsymbol{\mathrm{x}}\:−\:\mathrm{4}\mid\:−\:\mathrm{3}}\:\:\geqslant\:\:\mathrm{1} \\ $$

Question Number 207498 Answers: 1 Comments: 0

cos2x + sinx = tg(225°)∙(0,360°) sum of roots = ?

$$\mathrm{cos2}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{tg}\left(\mathrm{225}°\right)\centerdot\left(\mathrm{0},\mathrm{360}°\right) \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$

Question Number 207493 Answers: 2 Comments: 0

lim_(n→∞) (((n − 1)/(n + 2)))^(n+3) = ?

$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}\:+\:\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{3}} \:=\:\:? \\ $$

Question Number 207482 Answers: 1 Comments: 0

Question Number 207477 Answers: 0 Comments: 8

is there any generale form for this sequense { ((u_(n+1) =((au_n +b)/(cu_n +d)))),((u_m =k)) :} I need u_n in terms of n i have try to derrive it for a long time but i cant

$${is}\:{there}\:{any}\:{generale}\:{form}\:{for}\:{this}\:{sequense}\: \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{{au}_{{n}} +{b}}{{cu}_{{n}} +{d}}}\\{{u}_{{m}} ={k}}\end{cases} \\ $$$${I}\:{need}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}\:{i}\:{have}\:{try}\:{to}\:{derrive}\:{it}\:{for}\:{a}\:{long}\:{time}\:{but}\:{i}\:{cant} \\ $$

Question Number 207724 Answers: 1 Comments: 0

2 tg^3 x − 2 tg^2 x + 6 tg x = 3 , [0 ; 2𝛑] Sum of roots = ?

$$\mathrm{2}\:\mathrm{tg}^{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{2}\:\mathrm{tg}^{\mathrm{2}} \:\boldsymbol{\mathrm{x}}\:+\:\mathrm{6}\:\mathrm{tg}\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{3}\:\:\:,\:\:\:\left[\mathrm{0}\:;\:\mathrm{2}\boldsymbol{\pi}\right] \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$

Question Number 207723 Answers: 0 Comments: 2

lim∫_0 ^∞ (1−e^(−ncos(x)) )dx

$$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$

Question Number 207466 Answers: 2 Comments: 0

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