Irrational makes rational? Or does it? Part 2
Number Theory
Level
2
For all positive integer n,
Do there exist irrational numbers such that both their sum and product are rational?
No,but it is true for infinitely many of them.
No,it is true for only 2.
,YES,It is true for all natural number n
NO,it is only true for finitely many of them.
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1 solution
Take n pairs of conjugates i.e. pairs like ( a + b , a − b ) .
Then their pairwise product and sum both will be rational and hence,the problem statement will be true.