f a, b, c are positive real numbers such that a + b + c = 1, prove 8 8abc 27 (1a) (1 - b)(1 − c) ≤ -

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: Assume that 2< a < 3 and1<b< 2. Prove that: 2 < a? - 2 < 8. VI

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Q: Derive one-one correspondence between the real numbers in (0,1) and the set of irrational numbers in…

A: Both the sets that is real number in 0,1 and the set of irrational numbers in 0,1 are uncountable as…

Q: find a Positive integern for which the equality holds %3D

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Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

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: (a) Prove that (-1+iv3)" + (-1– iv3)" has either the value 2"+1 or the value –2" if n is any integer…

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Q: Find the set of real values of x for which a) > 3 by/2x- 3/ 0 13 Solve the inequality:x(x² – 6) >…

A: It is given that

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A:

Q: The numerical value of xe dr is

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

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Q: Prove that for all real numbers Ex)y= -(1u)

A: We have to prove that for all real numbers (- x)y= - (xy)

Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

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Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

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

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Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: For any integers a and b, a + b ≥ 15 implies that a ≥ 8 or b ≥ 8.

A: Let a+b≥15, where a,b are integers.   Case 1: b&lt;8 Then: b&lt;8⇒-b&gt;-8⇒15-b&gt;15-8⇒a≥15-b&gt;7…

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: If f(x) = x +l and g(x) = x-1 then the domain of (fog)(x') is a) All Real Numbers b) x21 c) IS1 d)…

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Q: (-1)"+1 1- 2n Given the set A = The infimum of A is

A: