Find all positive rational numbers x and y for which x + and y + - are natural numbers.

Q: Find two positive real numbers x and y such that they add to 120 and x2y is as large as possible.

A: Oue Aim is to find two positive real nnumbe x and y such that theyadd to 120 and x2y is as large as…

Q: Find two irrational numbers a and b such that a is rational.

A:

Q: 1:List all possible rational zeros of f (x) = x-5 x 2 –17 x + 21 Then determine which, if any, are…

A: Given,          fx=x3-5x2-17x+21

Q: . Assuming every number born on a finite day is a dyadic rational: lowest terms and r 2 0. Given two…

A: Two dyadic rationals, a / 2r < b / 2s where r is greater than or equal to zero. Now, we have to…

Q: Prove or disprove: The inequality 1/(2^x) ≤ 1/(x + 1) is true for all positive real numbers x

A:

Q: (b) Express in rational form the generating function of 2, -2/5, 2/25, -2/125, 2/625,..

A: The given problem is to find the generating function for the given sequence, we can observe same…

Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

A:

Q: Find all numbers for which the rational expression is undefined -En

A: The given rational expression is n3-6nn2-4.

Q: Let u be an nth root of unity. Show that u-1 is also an nth root of unity.

A: Solution:GivenLet u be an nth root of unity.  To Proveu-1 is also an nth root of unity.

Q: Find all numbers for which the rational expresnion is undefined +10 -v- 20

A: Given: The rational expression as  y2+10y2-y-20, To find: The value of y for the given rational…

Q: Show that there is no rational number r satisfying 2r = 3.

A:

Q: Prove that if x and y are rational numbers such that x > y, then there exists a rational number z…

A: We have to prove that If x and y are rational numbers such that x > y Then there exists a…

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A:

Q: Show that there are an infinite number of rational numbers between any two real numbers x and y with…

A: using Archimedean property to prove above therom...

Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

A:

Q: 6. Determine if the product of 3/2 and 8/18 is rational or irrational. Explain your answ

A: First we have to find the product of 32and818 Product = 32 × 818 = 2436 = 24×6  = 144

Q: Prove that the extreme value theorem doesn’t work over rational numbers.

A: Answer is mentioned below

Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

A:

Q: Ta) List all possible rational zeros of P.

A:

Q: Find all numbers for which the rational expression is undefined.

A: The rational expression is undefined when the denominator of the rational expression becomes equal…

Q: show that there doesnt exist a rational numbert such that t2 = 3

A: According to the given information, it is required to show that there does not exist any rational…

Q: Prove by reductio ad absurdum that there does not exist a minimum rational number greater than zero.

A: The proof by method of reductio and absurdum mean proof by contradiction . That is , you have a…

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

Q: The product of any non-zero rational number and any irrational number is irrational. For all real…

A: To prove the statement by using the method of contradiction, first assume that the conclusion is…

Q: The domain of a rational expression consists of all real numbers except those that make the

A: We have to complete the given statement.

Q: The set of all real numbers x for which x24x+2+x>0 is

A:

Q: The domain of a rational function is the set of all real numbers except those for which the…

A: The rational function is a function which takes a subset of real numbers as input and returns a…

Q: Let a, b, c, d be distinct real numbers such that a, b are roots of x - 5cx - 6d =0, and c, d are…

A: Given that, a,b,c,d be distinct real numbers such that,a, b are roots of x2-5cx-6d=0and c,d are…

Q: 3 Find all possible rational zeros of 4x° + 7 + 9x + 2. Write all answers as reduced fractions, and…

A: We will find out the required possible roots .

Q: Prove that x (x-2) is always a negative real number if x 1-Ai for some real number A.

A: The given number is  x(x - 2) x = 1 - Ai

Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

Q: For the pairs of integers a=13, b=32, find the gcd g and integers x and y satisfying g=ax+by. Attach…

A: Given that, the pair of integersa=13,b=32 The equation is: g=ax+by where g is the gcd.

Q: What are the remaining zeros of f  Degree 3; zeros: 8; 1-i

A: Answer is- Remaining zeros are 1+i So total 3 zeros which are 8,1-i,1+i. Explanation is given…

Q: Determine the rational roots of 2x 5 - 11x 4 + 14x 3 - 2x 2 + 12x + 9 = 0. 3/2 1/2 -9/2 -1/2 -1 -3…

A:

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: Determine between which consecutive integers the real zeros of Ax) = 3x - 5x² + 5x +7 are located on…

A: Given : f(x)  =3x3-5x2+5x+7 Interval [ -10 , 10]

Q: List all of the potential rational zeros of f (x) = 6x^(4)-9x^(3)+ 10x + 15.   precaluclus

A: The solution is given below

Q: 5=3+13メ-41x+3 2.

A:

Q: Show that the product of a non-zero rational and an irrational is irrational.

A: A number 'a' is said to be rational if 'a' can be written as,pq where p, q≠0 are integers. And, a…

Q: prove

A:

Q: Find all pairs of consecutive even positive integers, both of which are larger than 5 such that…

A: We have to find all pairs of consecutive even positive integers, both of which are larger than 5…

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: List all the possible rational roots of 4x-2x – 6x² + 22x – 15 =0. Show all work.

A: We need to use the rational roots theorem. It says that if we have a polynomial f(x) with integer…

Q: Find a rational number x and an irrational number y in the interval (0.119, 0.12).

A: Given: The interval (0.119, 0.12)

Q: Let x be a real number. Show that 1 [3x] = [x] + | x + - 3 3 ++1+

A:

Q: Find the rational number halfway between the two numbers below. 2. and- and is The rational number…

A:

Q: Find the number in {x E R:-2<x<2} such that the sum of that number and its square is a maximum.…

A:

Q: List all possible rational roots.

A: Given,   f(x)=2x4−3x3−9x2+8x+12

Q: 1 1 2 x y x+y || +

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.