If both product and sum of 2 positive reals are integers, are these reals necessarily integers individually?
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2 Answers
106(2+√3)(2-√3) = 1 = integer
2+√3 + 2-√3 = 4 = integer
but (2+√3), (2-√3) are not integers
simplest argument of contradiction
1i completely agree with bonne annee
this question doesnt make any sense because you will have infinite contradictory examples
Reason:
there exist infinite no of irrational nos between two rational nos
and the conjugate pair of any irrational no will satify both your conditions
i.e there will be infinite number of solutions which contradict the special condition of BOTH the nos having to be NECESSARILY INTEGERS
