5. By considering Z[¹+√5]*, or otherwise, show that if n and m are expressible as 2 a² + ab-b² and c² + cd-d², respectively, then nm is expressible as e²+ ef -f² for some integerse and f.

Q: 2 and B= 1 0. then Show that if A = 6. -1 2 (A + B)(A + B) # A² + 2AB + B?

A: Given that A=-1201 and B=10-12 We have to show that A+BA+B≠A2+2AB+B2

Q: verify that A(B + C) = AB + AC

A: Now,

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: Find AB if A = [4 -3 3 -1 0 -2] and B = 4 Use the tools in the

A:

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

A:

Q: (14x- 13) 4x + 13) (6x + 2)

A:

Q: MUI QUE If a and b are positive integers, which of the following can never be the gcd(56a, 63b)? (a)…

A:

Q: 3. Simplify (x+ 2)(x2+3x- 4).

A: (x+2)(x2+3x-4) = x(x2 + 3x - 4) + 2(x2 + 3x - 4) = x3 + 3x2 - 4x + 2x2 + 6x - 8 = x3 + 5x2  + 2x…

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: Show that x2+4x+17 is O(x3) but that x3 is not O(x2+4x+17).

A:

Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify.…

Q: a) 2x + 5 > 4x – 3

A:

Q: b) Find (3512, 2020) and find integers x and y such that 3512x + 2020y = (3512,2020).

A:

Q: verify that (A + B)C = AC + BC

A: To verify that (A+B) C = AC + BC.

Q: Consider the function f (same as in the previous problem) defined on the interval [0, 10] as…

A: Given Data: fx=35xx∈0,53x∈5, 10-y''=λy, y0=0, y'10=0To find: cn

Q: 1. (a) Prove that if alb and alc. then alb² + 10c + a.

A:

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: 2. Find the difference quotient of f(x) = 4x² – 7x + 5

A:

Q: 2. Determine all values of x - y when x and y are integers such that x = 360 + y².

A: The given equation is. x2=360+y2x2-y2=360x+yx-y=360 Since it is given that x and y are integers, so…

Q: For each positive integer n, define an = ((2+√3)" + (2-√3)") 2 It is known that an is a positive…

A:

Q: 3. Select all the statements that are true for any value of x. A. 7x + (2x +7) = 9x + 7 B. 7x + (2x-…

A:

Q: Multiply. (4x – 1)(3.r – 2) - O 11x – 12 O 12.x – 11 O 12.x2 + 11r – 2 O 12.x? – 11x +2 O 111? – 12x…

A:

Q: a) b) ab ac a + bc 3a 3 26 2. d) 1+ 2x 3x 똥 +

A: According to Bartleby terms I can solve only first question with first three subparts only  In these…

Q: Find integers x and y so that gcd(2021, 271) = 2021x + 271y. Find integers m and n so that gcd…

A:

Q: Evaluate the following * [x√x² - 7dx

A:

Q: 2. B = {1+x,1+x²₂x+x²} and x = 6 + 3x − x². Find [x]5-

A:

Q: 3. Which polynomial expresses the product of 4y(3y² +7y – 11)? O A. 12y³ + 7y – 11 о в. 12у3 + 28у —…

A:

Q: 3x3-5x2+5 Different iate with respect to X. x2+1 (x²+1)2 Different iate with respect to x. x2-1

A:

Q: 1 [(3x)2-1]2

A: We will use partial fraction to solve the integral

Q: a+2b 2 Let W = :a,be R}. Show that -4 lies in W. 2a -1

A: