Originally Posted by Idea abc=1 does not imply a,b,c is -1 or +1 as these are real numbers, e.g. a=1/3, b=2, c=3/2 , abc=1
As for the other question, a,b,c>0 is not an assumption. It follows from the given. Hmm, yea, you are right. But can you explain a bit how you got a,b,c>0 from given?
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Suppose a > 0 and b < 0 , c < 0
a^2 - a = b + c - b^2 - c^2 < 0 implies a < 1 and bc > 1 since abc = 1
( b + c )^2 >= 4bc > 4 so that b + c would be less than -2 and so a + b + c < -1
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