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Wednesday, March 15, 2017

A property of sides of a triangle?



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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