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This question must be limited to a and b being integers, otherwise there are infinite sets of solutions to this question, for example: a=1,b=7/3;a=2,b=6/5... ...
you can find all real solutions in less than 10 seconds using AM-GM Inequalities. the answer is a+b>=sqrt(17)-1 or a+b=sqrt(17)-1 or x=sqrt(17)-1 or a+b
How about adding eqns in each case?? I think there were no conditions of a and b. So, I think adding eqns is better than soluting a and b in each case.
