In Z[√ 2] = {a + b√ 2 | a, b∈ Z}, show that every element of theform (3 + 2√ 2)n is a unit, where n is a positive integer.

Q: If the A.M. and G.M. between two numbers are in the ratio mn, then prove that the numbers are in the…

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Q: Which theorem can be used to prove that ARQM APMQ H R P M

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Q: Rationalize the numerator of √x -4 √√x √√√x-4 √√x Question 15, 10.5.77 HW Score: 33.33%, 5 of O…

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Q: -7x Sre™-3 + x + x = 1 dx The 3x لوکی

A: Topic:- application of integration

Q: 4. Find all the values of the indicated roots a) √4 | b) √√-1-i

A: Step 1:Step 2: Step 3: Step 4:

Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: +a2+C √ √√a² + u²du = ½ (u√u² + a² + a²]n]u + √u² + a² 1) + T 114

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Q: Show that if |z1| ≤ 2 and |z2| ≤ 3, then one has |(3+4i) 2₁ (1 + i)21 22 ≤ 10+6√2 21 -

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Q: z = (a + bi)4n+ (b + ai) 4n; a ∈ ℝ ; b ∈ ℝ; n ∈ ℕ. Show that z is a real number.

A: Properties of complex number : If z is real number than z=z¯ . Suppose z=x+i y than z¯=x- iy .…

Q: 2. Let Z [√2] = { a+b√2 la,be Z}. Define addition and multiplication on Z[√2] as follows: (a+b√2)+(c…

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Q: Let u = (5,5,0) and v= = (5,5,5√√2). Compute |uxv|. Then sketch u, v, and uxv. |uxv= (Simplify your…

A: I have explained everything with in the solution. Please go through that.

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

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Q: 1. Let a, b € Z so that 2a + 3b is a multiple of 11. Prove that 11 divides a - 46.

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Q: 3 1 2 8 √x³ 3 2 1 3 X 3 X2 ; 2 - x > ; x ≥ 0x 3 X

A: Given :x31x23x321x-1

Q: h9HXth*x f3.1) he mt itextsS St ,2)

A: Given:

Q: Prove that

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Q: 3. Let r be a real number. Prove by contrapositive that if r+4x <35, then z < 3.

A: Note: Proof by contrapositive: If we want to prove that "if A, then B". Then we use contrapositive…

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: Prove that if 0 < a < 1 and b = 1-√1-a, then 0 < b < a.

A: To prove If  and  then

Q: Which of the following statements are correct for the pde -2uxxx +3vxt-7u, = e sinx Auft A) Linear,…

A: This question  is about  partial  differential equation

Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

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Q: Show that Q(√5, √7) = {a+b√5 +c√7 + d√√35 | a, b, c, d € Q} = Q(√5 + √7).

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Q: Q24 prove that b) 3i 3i √2+i √2-i = 2 ?

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Q: 1. If a = 37 – 43 + k 2a - 36 a) 2 and 6 = -27+33 - k 7 b) a +56 express each of the following terms…

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Q: A) |2x² + 5x + 1 = 1 B) 12/1 x-1 x+1 C) 5x + | ≥ 1

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Q: - [a C b If A = where a, b, c and d are real numbers, then prove that A²-(a + d)A + (ad-bc) I=O.…

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Q: Let w = √√x + y²z³, x = 1 + u² + v², y = uv, and z = 3 Findow and w ди av

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Q: Let ü = 21 – k and i = i + 3j + k. Compute |ū], |ū], ū × ĩ, and Projzu.

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Q: 1 2√n+1 ≤ √n+1-√n ≤ 1 2√√ñ

A: The given problem is from inequalities.We will solve this problem by using the intermediate value…

Q: Let a, b e Z so that 2a + 36 is a multiple of 11. Prove that 11 divides a - 4b.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.