Let Q be the field of rational numbers and let F Q(√2, √7). You may assume that √2, √7, √14 are irrational. (a) Show that √7 Q(√2). Hence obtain that [F : Q] = 4.

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Q: a. If p=√q=ra and pqr = 1, show that, x + y + z = 0.

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Q: Assume xo = x2 – 2h, *1 = 12 – h, a3 = x2 + h, 24 = x2 + 2h Use the undetermined coefficients method…

A: To solving the system we use the Gaussian Eliminating and back substitute method

Q: Define w := 1/2+√³,0 = -1/2 + √5, and 7 := " 1+5. Determine IQ[W,0,7](Q).

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A: Please note :    According to our Company guidelines we need to solve only the first one.Please ask…

Q: 03- If z = 1-√√3i 1+√3i then find zz ?

A: Given .We have to find the value of .

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Q: QI: using the Bairstow's method to find a complex root for f(x) = 50 – 8x - 62x + x*, where (x2) is…

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Q: Let A = 2 3 4 1-3 5 Find the following: (a) (DA)T and B = 1 5 2 -1 0 1 3 24 and C= (b) 2C+C² 4] 6 -2…

A: The matrixes are :The main aim is to find :a) b)

Q: (x + y = 1 (2x + y = 3 3. Solve the system for vectors in the field Z,.

A: To Determine :- The system of equations  x + y = 12x + y = 3 for vectors in the field ℤ7.

Q: Given P₂ = { a+at+at² | ª, ª, a are reals } B= {1-1², t+t², 2-t-t²} and E= {1, t, 1²} [1] Show that…

A: Given:  B=1-t2, t+t2, 2-t-t2 E=1,t,t2 To find: The E coordinates of qt where qB=-123 using change -…

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A: We need to find the principle part of  for  with respect to .We know that the principle part  of…

Q: Part 1: Solve using Cramer's rule. 2x1 + 6x2 = 26 6x1 + x₂ = -24 Part 2: Calculate the area of the…

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Q: (25. The roots of g(x)= 0 are iwo times the reciprocals of the roots of x"-- 7x + 3 = 0. g{x)= A. 3x…

A: Let α and β are the roots of the equation  ax2 + bx +c = 0 then,   Sum of roots =(α + β) = -b/a…

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Q: Find the 5th roots of 9. -16/2 + 16vZi

A: =12+32i9De Moivre's theorem;=cosπ3+i sinπ39= eiπ39=ei3π=cos3π + isin3π=-1

Q: implified?

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Q: 2. Factor the polynomial: 300y z- 60-4x +432°. _

A: The solution for the above question is as shown below.

Q: Why did we plug in x = 1/2 at the last part of the solution for the second problem

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Q: (d) Let Z₁ = −4+ 8i and Z₂ = -1 -2i. Show that (i) 21/2₂ | = 4. | (ii) (iii) |z₁|² +Z₁ Z₂ = 100.…

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Q: 2(8z¹y) = ? 1) None of the choices here are correct 02)-2x¹/3y6 031-21 04) 221/36

A: Now,  we  can write ,the  given expression as  2(8)-23 ×x12-23×y9-23Recall  fact that  amn=amn  and…

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Q: - Find the zero and its order for the function f(2)=1-Ti+Z+e.

A: Note: If W is the Lambert function then Wxex=x

Q: LAR널)] = Y(S) = [올 +2 Yi(s) = Y,(s) = (S+4)×2 블 +8S+20 N/A ( 52 ) ³²+ + 4 . √2 + 5 - S14 (S+4) e (5²…

A: To show:-

Q: 5) Solve by Cramer's Rule. Show all your work. (x=y+2z= 0) 3x +z = 11 (-x + 2y = 0)

A: By using cramer's rule we have to solve given linear system of equation.

Q: 10 - Which one is the highest order Lagrange polynomial of the grids below? Xị Yi -2 3 1 -1 x2—9х-8…

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A: Diaphantine equation

Q: 12. Solve for x. a) 를x-3=x+ 2 b) 쓰= c) (x +1) = (x – 3) x+5 2x-1 3 d) -5(x + 1) – 2(x + 1) = 3(2x –…

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Q: Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a…

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Q: For what values of a and b are x +1 and x +2 factors of xr² ax-bx -82 Write down the other factor.…

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Q: Can someone explain how this problem is simplified with steps: ((x2 + y2 + z2)1/2) - (x2 / (x2 + y2…

A: In this problem we simplify by taking LCM on left hand expression & hence we get the result on…

Q: O 22 I √x+1= ?

A: Given data

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Q: Evaluate Answer: dt t² + t-30 S₁

A: ∫1t2+t-30dt

Q: ³₁(1+w) (2w + w²)5 dw

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