Ravi's Substitution
c + a − b a + a + b − c b + b + c − a c
If a , b and c are the side lengths of a triangle, find the minimum value of the expression above.
The answer is 3.
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1 solution
U can also use the inequality
( a + b − c ) ( b + c − a ) ( c + a − b ) ≥ a b c
I'm not quite sure what you're doing here.
You seem to go from ( a − b ) 2 + ( b − c ) 2 + ( c − a ) 2 ⇒ a ≥ b ≥ c ≥ a which is not true. Note that the first inequality is true for all real triples.