If d is a positive and not perfect square integer in [6,8]. Assume that √d = [ao; a₁, a₂, 3, 1, a5]

Q: 23. For any real number a, a ‡ 0, show that a +1 a +4 a +7 a +5 a+6 a +9 a -2 a +3 and a +8 | = 0, a…

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Q: Let H = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f} Let W = {(a, b) : a € H, b = H} be the…

A: Answer:-

Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

A: We are required to prove: a+1a+4a+7a+2a+5a+8a+3a+6a+9=0a4a7a2a5a8a3a6a9a=0aa4a7a2a5a8a3a6a9=0

Q: Prove. Z40 (Rez) ² +Z1 ? 0

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Q: perform the indicated calculations 2[2, 2, 1] in Z33

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Q: . If an+2 = 6an+1 - 8an + 3 and ao = 3, a1 = 7, then a6

A: We have to solve given problem:

Q: . Let n = 2 and m > 2 be integers, and let a and b be real numbers. Which of the following is not a…

A: To check: Which of the following is not a property of radicals: Formula rule: Exponent rule:…

Q: Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

A: we have 15a+20b =49 and a and b both are in R  we prove that a and b are not both integers.

Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

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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: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

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: Let a, b, and c be natural numbers. Prove a ∙ (b + c) = a ∙b + a ∙ c.

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Q: If c = (−3, −5) and ♂ = (–2, −6), find |4č – 2.5d|. O √74 O √146 O 7√5 O 8√6

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Q: 1. Prove that the sum of an integer and its square is even

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Q: 2. Show that for all positive real numbers a and b, if a < b then a² < b².

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Q: a a + b Determine all values of a and b so that belongs to а 1 3 1 Span 1

A: We have