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Question Number 156579 Answers: 1 Comments: 0

Find the value of x by using Cardon′s Method. (1/x) + (2/(x+1))+ (3/(x+2)) = 1

$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{Cardon}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{Method}}. \\ $$$$\:\:\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\:+\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}+\:\frac{\mathrm{3}}{\boldsymbol{\mathrm{x}}+\mathrm{2}}\:=\:\mathrm{1} \\ $$

Question Number 156578 Answers: 0 Comments: 0

Question Number 156577 Answers: 0 Comments: 4

Question Number 156575 Answers: 1 Comments: 1

let n≥1 and λ=2n^2 -2n+1 solve for real numbers: (√(λ + x^2 )) - (√(λ - x^2 )) = (x^2 /n)

$$\mathrm{let}\:\:\mathrm{n}\geqslant\mathrm{1}\:\:\mathrm{and}\:\:\lambda=\mathrm{2n}^{\mathrm{2}} -\mathrm{2n}+\mathrm{1} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt{\lambda\:+\:\mathrm{x}^{\mathrm{2}} }\:-\:\sqrt{\lambda\:-\:\mathrm{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}} \\ $$

Question Number 156574 Answers: 0 Comments: 0

if a;b;c>0 and (1/(a+b)) + (1/(b+c)) + (1/(c+a)) = 4 then: (1/a) + (1/b) + (1/c) + (9/(a+b+c)) ≥ 16

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{b}+\mathrm{c}}\:+\:\frac{\mathrm{1}}{\mathrm{c}+\mathrm{a}}\:=\:\mathrm{4}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}}\:+\:\frac{\mathrm{9}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:\geqslant\:\mathrm{16} \\ $$

Question Number 156600 Answers: 2 Comments: 0

∫ (e^x /(e^(2x) +4)) dx =?

$$\int\:\frac{{e}^{{x}} }{{e}^{\mathrm{2}{x}} +\mathrm{4}}\:{dx}\:=?\: \\ $$

Question Number 156557 Answers: 0 Comments: 1

Question Number 156548 Answers: 1 Comments: 2

Question Number 156543 Answers: 0 Comments: 0

Question Number 156536 Answers: 0 Comments: 0

Question Number 156535 Answers: 1 Comments: 0

Question Number 156534 Answers: 2 Comments: 1

Question Number 156532 Answers: 1 Comments: 0

Question Number 156529 Answers: 1 Comments: 0

Question Number 156522 Answers: 0 Comments: 1

Question Number 156520 Answers: 1 Comments: 0

if ∣ z+6i ∣≤5 find the maximum and minimum value of ∣ z+5∣ ?

$$\boldsymbol{{if}}\:\mid\:\boldsymbol{{z}}+\mathrm{6}\boldsymbol{{i}}\:\mid\leqslant\mathrm{5}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{maximum}}\:\boldsymbol{{and}}\:\boldsymbol{{minimum}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\mid\:\boldsymbol{{z}}+\mathrm{5}\mid\:? \\ $$

Question Number 156513 Answers: 0 Comments: 3

x^4 +4x^3 −26x^2 −20x+25=0 x=? (exact form)

$$\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{3}} −\mathrm{26x}^{\mathrm{2}} −\mathrm{20x}+\mathrm{25}=\mathrm{0} \\ $$$$\mathrm{x}=?\:\left(\mathrm{exact}\:\mathrm{form}\right) \\ $$

Question Number 156511 Answers: 2 Comments: 0

Question Number 156517 Answers: 1 Comments: 0

∫ (dx/(3tan x+cos x)) =?

$$\int\:\frac{\mathrm{dx}}{\mathrm{3tan}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:=? \\ $$

Question Number 156509 Answers: 1 Comments: 5

Question Number 156508 Answers: 1 Comments: 0

Question Number 156507 Answers: 0 Comments: 0

Question Number 156502 Answers: 1 Comments: 0

Solve for integers: (x^2 + y^2 )(x^4 + y^4 ) = (x + y)^6

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{integers}: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \right)\:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{6}} \\ $$$$ \\ $$

Question Number 156495 Answers: 1 Comments: 0

1. Write the first three terms of each of the following sequences: (a) a_n = (3^n /(2^n + 1)) (b) a_n = (−1)^(n−1) n^3

$$\mathrm{1}.\:\mathrm{Write}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequences}:\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{a}_{{n}} \:=\:\frac{\mathrm{3}^{{n}} }{\mathrm{2}^{{n}} \:+\:\mathrm{1}}\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{a}_{{n}} \:=\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {n}^{\mathrm{3}} \\ $$

Question Number 156485 Answers: 0 Comments: 0

2021! Σ_(n=0) ^∞ Σ_(k=0) ^∞ (1/(Π_(m=1) ^(2022) (n + k + m))) = (1/A) Find the value of A

$$\mathrm{2021}!\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\mathrm{2022}} {\prod}}\left(\mathrm{n}\:+\:\mathrm{k}\:+\:\mathrm{m}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{A}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{\mathrm{A}} \\ $$

Question Number 156475 Answers: 1 Comments: 4

soit:∫_o ^x f(t)=x+∫_0 ^x t^2 f(t)dt determiner f(1)

$${soit}:\int_{{o}} ^{{x}} {f}\left({t}\right)={x}+\int_{\mathrm{0}} ^{{x}} {t}^{\mathrm{2}} {f}\left({t}\right){dt} \\ $$$${determiner}\:{f}\left(\mathrm{1}\right) \\ $$

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