+ Prove that if a is a nonzero real number, then 1. 25z? 1 (Hint: Start with the inequality (a - 20, which is true for every nonzero real number r.) 5x

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A: Given, sum of two numbers are 62. Let one of them is x, then other will be (62-x). Product of these…

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A: False.    conjecture. For all number x, x4 > x

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A: Note that |x-4| is an absolute value. So it will be always greater than or equal to 0.  If it equals…

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n-3 17 ac² cn-4 с - в n=3

A: The given series can be written in Geometric series form, Put…

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Q: simpfly. all postive exponets and assume all numbers are postive, real numbers.  (z^3 x)^1/6 over…

A: Given,

Q: What two nonnegative real numbers with a sum of 50 have the largest possible product? The numbers…

A: We are asked to find the largest possible product of the two non negative number whose sum is 50

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 112m-3 4 - c" 4 ac?

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Q: 6. Use a direct proof to show that if a and b are positive integers, then +2 2. Hint: Rewrite the…

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Q: What is the supremum of the set consisting the following real numbers: 0.1222...,…

A: Given Set of Numbers {0.1222....,0.2122...,0.22122....,0.222122...,........} Supremum of this set is…

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A: Irrational numbers cannot be negative.

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A: Yes, the product of  even integer and any integer equal to even

Q: Using a direct proof, prove the following statement: For any real number x, 20(x – 1) = 4x²+ 5

A: Using a direct proof, prove the following statement: For any real number x, 20(x – 1) = 4x²+ 5

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n- 3 17 00 ac? с — в

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Q: Pzif akb then [a,b]-(- All of a,b are in real numbers

A: The given statements are: p: a&lt;b q: a, b=(-∞, b] \ -∞, a Prove: If p, then q. If a&lt;b, then  a,…

Q: What two nonnegative real numbers with a sum of 66 have the largest possible product? The numbers…

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Q: 4. For the incquality 3n+1> n° determine the set of natural numbers for which

A: Introduction: For all-natural numbers, the principle of mathematical induction is a concept that…

Q: State all integer values of x in the interval [-1, 5] that satisfy the following inequality: 5x – 5…

A: 5x -5 &lt;-2      Interval -1 , 55x -5 &lt;-25x -5+5 &lt; -2+5         Adding 5 on both…

Q: Choose what method of proof to use always provide solution.   a) Prove that if the sum of any two…

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Q: 0. Is it possible to find nonzero whole numbers m andn such that 11" = 13"? Explain. %3D

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Q: V5 +3 v3 - E-2 where k is an integer to be found. V5 + V3 Without using a calculator, show that Cs…

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Q: Consider the following statement. There are real numbers a and b such that Va +b = Va + vb. To prove…

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Q: Let c, a, ß be nonzero real numbers such that e + B. Find a given that 2n-3 ac 11 c - B'

A: Given, c,α,β be nonzero real numbers such that c≠β, To find the value of α such…

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A: Let the two numbers be 'a' and 'b' Let the GCD of the numbers 'a' and 'b' be 'G' Then we can write…

Q: Make a conjecture! Is 2*<2* always true? If not, provide a counter-example.

A: In the given inequality, to check whether it is true or not, first, take some value of x and check.…

Q: 4. Prove or Disprove Prove or disprove that for all real numbers a and b, if a? = b² then a = b. %3D

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Q: Suppose that m andn are positive integers and b is a real number so that the principal n" root of b…

A: We have been given that nth root of b exists where b is the real number.

Q: State all integer values of x in the interval -3 3

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Q: set of positive real numbers between 1 and 3

A: There are two ways to define sets. In first, we include 1 and 3. In second, we exclude 1 and 3.

Q: Let a, b and c be integers that satisfy 1 1 1 - - - - a b C |(A) 2022 (В) 2025 Find one possible…

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Q: What two nonnegative real numbers with a sum of 46 have the largest possible product? The numbers…

A: The objective is to determine what two non-negative real numbers with the sum of 46 have the largest…

Q: 9. On a real number line, label the points with coordinates of 3 0,1,–1,-,-2.5,- and 0.25 4 2

A: The graph is shown in next step.

Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: Select all the real numbers M among the choices below such that the two planės glven by 3D2 and ()-…

A: We can solve this by using given information

Q: What two nonnegative real numbers with a sum of 64 have the largest possible product? The numbers…

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Q: Please help me to write this as a proof.  Let n be an integer. If n is the sum of three consecutive…

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Q: For which positive integers $n$ greater than or equal to 2 is $\sqrt[n]{a^{n}}=a$ always a true…

A: We need to check for all the values to get the result

Q: (a) Prove that ANBCANB.Give an example to show that equality does not always hold.

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Q: R.2. Prove that for every real number x, if x 0 and x +1 then there is a unique real number y such…

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Q: Fiad the tonstantterm 12 x - 2013 Leave the answer in biñomial coeffient

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Q: Pls kindly help to prove: when n is even, then (n, (n/2)^2-1, (n/2)^2+1) will be a Pythagorean…

A: Given question is  prove: when n is even, then (n, (n/2)^2-1, (n/2)^2+1) will be a Pythagorean…

Q: . Show that there exist no nonzero real numbers a and b such that va² + b? = Va³+b.

A: To remove the radical sign in the equation a2+b2=a3+b33, raise the power to 6 on both sides of the…

Q: 5. (10 points) Prove that for all positive real numbers r and y, one has the inequality > 2 (u+ 112…

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Q: . Use a direct proof to show that if a and b are positive integers, then +2 2. Hint: Rewrite the…

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Q: Prove that the absolute value of the product of two integers is equal to the product of the absolute…

A: Prove that the absolute value of the product of two integers is equal to the product of theabsolute…

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 152n–3 Σ2 ac? cn-4 с — в n=3

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 16?n-3 20 ac² cn-4 с — В n=3

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Q: If 5x – 8 = 12, then x = 4. Statement Reasons

A: Given: if 5x-8=12, then x=4 For verifying the solution of given expression, we simplify given…