Prove that there is a positive number z so that z^5 + 10z = 10.

Q: The answer is incorrect because the question requires to prove it without fully expand the terms.…

A: This question can be solved using the concept of general term of binomial expansion.

Q: Find the fourier expansion for the function whose definition - - <x <- 2 x, - 2 (x) 0, <x< 2 2

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Q: 11 Prove that

A: Laplace Transformation: Given a function Ft defined for all real t≥0, the Laplace transform of Ft is…

Q: find a Positive integern for which the equality holds %3D

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Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

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Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: Prove in an integral domain, a prime element is always irreducible.

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Q: 2. prove that

A: I solved through matrix form.

Q: Use Fermat's Theorem to find a number x between 0 and 28 with x 85 congruent to 6 modulo 29. (You…

A: as given  x85≅6mod 29   ...i as we known 29 is a prime number  by fermat's little theorem if p is a…

Q: Use Euler's Theorem to find a number x between 0 and 28 with x85congruent to 6 modulo 35. (You…

A: Here finds the value of x for which: x85≡6mod35 and x lies between 0​  to 28

Q: LI) Prove that (3

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Q: (List all irreducible polynomials of degree < 2 in Z3 [x].

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Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: -, first prove that )" 6.

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Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: Prove Simple disprove is Bing That Characteristic af Prime or either Zero or

A: A simple ring R is a ring with unit such that the only two-sided ideals are R and (0). The…

Q: show that: (For real nu

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Q: Prove that 1- coshx=In(x+ -x=In(x + Vx² -1 |

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Prove Theorem 11.3

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Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: f for ƒ : R - {2} → R- { 5} indicated by f (x) =(5x +1)/(x -2a), a bijection can be made from [0, 1)…

A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: Prove that the product of two odd numbers is odd.

A: We first define a general odd number. Lets say that n is an integer. When we multiply any number by…

Q: Find the integral from -5 to 7 -5 -4 -3 -2 -1 1 2 34 56 7 -3

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: All Fermat's number is clearly odd numbers

A: Fermat number.

Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: 6. Prove that ER, # 0.

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Q: Let 2k +1 be a prime number. Prove that then k = 0 or k = 2" for some n > 0. %3D

A: Solution:- Let 2k+1 be a prime number k=0 or k=2n for some n≥0   For, k=0 2k+1=20+1 2k+1=1+1…

Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: Prove that (1-x*)у ,-ху, +р'у-0

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Q: Find 2 pOsitive real numbers x and y such that their s um is 40 and their product is as large as…

A: SOLUTION-

Q: Find [7]^-1 in Z55 under multiplication.

A:

Q: Prove

A: To prove  tanxcosec2x-tanxsinxtanx+cosx=cos2xcosecx

Q: Prove That Cn) =nsh ツールがー

A:

Q: Express x8 - x as a product of irreducibles over Z2. Please be clear, correct and legible. Thank…

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Q: Show that 1 sech-1x = In x2

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Q: Prove that 1 + sqrt5 is irreducible and not prime in z [sqrt5]

A: I have used the definition of prime amd irreducible elements in ring

Q: coth- x = In () Q1/ Prove that

A: To prove coth-1x=(1/2)ln[(x+1)/(x-1)]

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: find integral of 8xsin(4x2)

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Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: Express x8-x as a product of irreducibles over Z2

A: We have to express x8-x as a product of irreducible over Z2. Definition:- Irreducibility is defined…

Q: how that all the irrational numbers in the interval [0, 1] is dense there.

A:

Q: A complwx number z is a number of the form z=x+iy, x,yER

A: Both the statements are TRUE

Q: How many words of lengthn≥6 in the alphabet{1,2,3}contain at least two of each digit?(Prove a closed…

A: Here we have to find the total number of possible ways of length n≥6 in the alphabet {1,2,3} contain…

Q: 3. Prove that the sandwitch theorem.

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Q: Prove that 1 tan 7 1 + tan tan 13 9.

A: Given : tan-117+tan-1113 = tan-129