Prove or disprove:
Proposition: a,b,c are sides of a triangle if
(a+b+c)(1a+1b+1c)<10
Note that we can easily show that (using AM ≥ GM for instance)
(a+b+c)(1a+1b+1c)≥9
for any positive reals a,b,c.
So we can restate the above statement as
Proposition: a,b,c are sides of a triangle if
⌊(a+b+c)(1a+1b+1c)⌋=9
where ⌊x⌋ is the integer part of x.
[Note: Initially I had if only if, but I have changed the statements to just be an implication]
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