Let a₁, a2,,an be positive real numbers. Pra

Q: Prove: Let a > 0 and b > 0 then either a > 0 and b > 0 or a < 0 and b < 0. where a…

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 32n-3 4 Cn-4 ac? c - B n=3 O…

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Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Prove that a b + 2c + 3d + c+ 2d + 3a Let a, b, c, d be positive real numbers. C d + 2a + 3b + d a +…

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Q: Prove that if a,b belong R(Real Numbers) then |a|-|b| is lesser or equals to |a-b|

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Q: Is 3 A m, m being any real number, possible? Explain. [IC]

A: This is a problem related to vector parts. Based on the general formula and concepts we will answer…

Q: at a, b and c be real numbers such that a #0 and ac+bc+c 4ac.

A: Given data is : a , b and c are real number such that a≠0 and ac+bc+c2<0 Show that b2>4ac

Q: Let x be a real number. If 2x2 + 1 is irrational, prove that x is irrational.

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Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: et a, b, c be positive real numbers. a² 6² c² a c

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Q: f x and y are two positive real numbers, then there exists a positive integer n such that ny>x

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

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Q: For a real number a, if a + 0 then a x a E R+.

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Q: Let A be a set of n real numbers. Show that A+ A- A € (n).

A: As per the question we are given a set of n real numbers A and we have to show that : |A + A•A| =…

Q: 4. Show that Archimedean Principle is a consequence of the assertions that every interval (a, b)…

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Q: (a) f '(x) = 0 X0 O x1 O x2 O x3 O x4 O none of these f "(x) = 0 (b) O xo O x1 O x2 O X3 O X4 O none…

A: To solve the following problem

Q: IfÂ=ax+ißP,, where a and B are real then (axR+1BP,x]is -hB

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Q: prove the following statement.

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Q: 3. Show that Z, -

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Q: For positive integers a and b, show that a ab

A: Consider the provided question, For positive integers a and b,  we need to show that, xab=xab

Q: Give an example of numbers a and b such that |a + b| < |a|+|b|.

A: To give an example of numbers a and b such that