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KingCalc
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Homework Statement
Prove that if 0 < a < b, then
[tex]a < \sqrt{ab} < \frac{a+b}{2} < b[/tex]
Homework Equations
Axioms (Properties), courtesy of Wikipedia:
Addition:
P1: For all a, b, and c in F, a + (b + c) = (a + b) + c
P2: There exists an element of F, called the additive identity element and denoted by 0, such that for all a in F, a + 0 = a
P3: For every a in F, there exists an element −a in F, such that a + (−a) = 0
P4: For all a and b in F, a + b = b + a
Multiplication:
P5: For all a, b, and c in F, a · (b · c) = (a · b) · c
P6: There exists an element of F, called the multiplicative identity element and denoted by 1, such that for all a in F, a · 1 = a
P7: For any a in F other than 0, there exists an element a^(−1) in F, such that a · a^(−1) = 1
P8: For all a and b in F, a · b = b · a
P9: For all a, b and c in F, the following equality holds: a · (b + c) = (a · b) + (a · c)
The Attempt at a Solution
I really just don't know what to do. A small push in the right direction could make all the difference. Thanks to anyone that replies and helps.
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