- #1
armolinasf
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Homework Statement
Prove that if a,b > 1, then a+b < 1+ab
The Attempt at a Solution
Just want to know if this makes sense:
first let a+b < 1+ab become 1<(1+ab)/(a+b) ==> 0<(1+ab-(a+b))/(a+b).
Factoring the numerator: 0<(1-a+ab-b)/(a+b) ==> 0<(1-b)+a(b-1)/(a+b)
So the next step would be to figure out where the numerator is greater than zero, since that is equivalent to our original inequality (do we just ignore the denominator since its undefined only in relation to variables?).
Solving the numerator for b would be: 0<(1-b)+a(b-1) ==> -(1-b)<a(b-1) ==> 1<a
Would this be an acceptable proof?