d/ Prove that the following numbers are real (for any 3 享

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

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

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Q: For some real numbers m and n, the list 3n2, m2, 2(n + 1)2 consists of three consecutive integers…

A: For some real numbers m and n, the list 3n2 ,  m2  , 2(n + 1)2  consists of three consecutive…

Q: Step by step else downvote, with clear handwriting. Prove that for any real number x, there exits a…

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Q: true or false

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Q: Show that V12 is irrational

A: A Rational Number is a number that can be written in terms of P/Q.  An irrational number can not be…

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: FIND AUB,GIVEN THAT A= {x/x is a positive integer. 2<x<6}    B= {x/x is a negative integer, - 6<x<…

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Q: Find A.

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Q: 上耳 7. 2 2 J ancd Re, .3 4 . 3 find p+Rt[tP+P}+R]+ [P+ (@+R}]reR

A: Given P=2316, Q=1234 and R=1231 1) Q+R=1234+1231         =1+12+23+34+1         =1465 2)…

Q: Evaluate each of the following for x = 5, 7, 9 and 2. ∑x2 ∑x2 – 5  ∑(x2−5) 2∑x2- 5  2(∑x2- 5) 2)

A: Given:   X = 5, 7, 9, and 2.

Q: 3.54. If the arithmetic mean of two unequal positive real number 'a' and 'b', (a > b), be twice as…

A: In question, Given that the arithmetic mean of two unequal real numbers a and b be twice of their…

Q: For each positive integer n, find with proof GCD(220° - 220, 220" + 218).

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Q: Show that 2 + V5 is imational number

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Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can…

A: We will use standard division algorithms to deduce the given statement.

Q: Show that these three statements are equivalent, where a and b are real numbers: (i) a is less than…

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Q: prove the following statement.

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Q: Determine: 1 (1 -1 2] [2 3] +0 1

A: given  1-124-1023+1001-1-1 solution we will use property of matrix multiplication and addition to…

Q: Show that 5 – V7 is an algebraic number.

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Q: Prove that the number V7 lies between 1 and 2.

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Q: Find five consecutive odd integers such that when the fifth is subtracted from eigt times the…

A: We're going to solve

Q: Disprove this statement by giving a counterexample. For all nonzero real numbers, a, b, c, and d,…

A: Here a,b,c,d all are non zero real .So (a/b) and (c/d) are defined.  Let,  a = 1 , b = 2 , c = 3 , d…

Q: L (21 +x+3)dx

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Q: Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number?…

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Q: 2. Show that for any real number x, if x + 2 > 10, then x? – 14 > 5x. Use direct proof.

A: