(7) Are the following ideals.Prime, Maximal or neitherin the rings R? Why?R = 26x12(a) (x+5),(b)22x+4> R=22 [²]R = Q[²]224x521, R = 21 x 21(e) 71 x 7 26, R = 21 x 21(f)(c) <2x+4>,{a+b√3|319}, R = 2/(√3)Татов

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Answered: (7) Are the following ideals Prime,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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B and D please
11. - What is the conjugate of 21√√5 – 3√3? a) 2√√5+ 3√√3 - b) 2√√53√√3 - c) = 2√5 - 3√3 d)3√3-2√√5 Which of the following rational functions has a slant (oblique) asymptote? 12. a)y = 2 x-3x+2 3x³-2x²+4x+1 b) y = 4x²-1 2 2x-x+1 c)y = 3x³-2x²+4x+1 4 3 2 5x +x+2x +8x+2 d) y = x²+x+1 2 2 x +4x+2
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Where Q is the field of rational numbers. Such that Q(√6) =a+b(√6) Where a and b are rational numbers.
Solve the question in 20 m8n plz i need urgent and perfect soloution plz
2x a) lim- x-3 x+ 1 x² – 4x + 4 b) lim х-2 х2 + x-6 у? — 4у — 21 y-7 3y2 – 17y – 28 t3 + t2 – 5t +3 c) lim d) lim t-1 t3 – 3t + 2
1. Find the locus of the equation /z-2+4j/=3/z/ and state the shape 2.using demoivre principle expand (1/2 + j√3/2)¹³ 3.find the root of the polynomial given that one of the root is 2i in x⁴+x³+5x²+4x+4=0
(6) Recall that a subset A of RP is dense in RP if Ã = RP. (b) Use Newton's method to construct a sequence of rational numbers con- verging to √2. Google "Newton's method", or consult a reference, if you are unsure what Newton's method is.
k Find the quotient using the long division method. Show the solution on the ; provided. 1. х — 2)x - 3х + 4 x + 3)x³ + 2x2 + 4x – 1 2. 3. х + 4)x3 - Зx? + 2х + 9 x - 5)x* - 2x² – 4x + 8 4. х—
Pls help solve this. Thank you!!
(d) Explain why the following "proof" is incorrect: "Claim: The integral domain R = {a+b√√2 | a, b = Z} is not a unique factorisation domain. Proof. In R we have the factorisations 2 = √√2. √2 and 2 (2+√2) (2 - √2). These are two different factorisations of the element 2 Є R, which shows that R is not a unique factorisation domain." (e) Is the element 7+ 5√2 a unit of the integral domain R = {a + b√√2 | a, b = Z}? Justify your answer.
Prove that for every positive integer n there exist polynomials of degree n that are irreducible over the rational numbers. (Hint: xn-2) Please include step by step solution with explanation. Thank you.

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(7) Are the following ideals Prime, Maximal or neither in the rings R? Why? (a) (x+5) R = 216x² (2) (3) 22x+4 R = 2(²) (c) <2x+4), R = Q[²] (d) 221x521, R = 21 × 21 (e) 26 × 726, R = 24 x 24 (f) { a+b√3 [319}, R = 21 [√3)