How can I prove that nonzero integer linear combination of two rational independent irrational numb

Joel French 2022-07-01 Answered
How can I prove that
nonzero integer linear combination of two rational independent irrational numbers is still a irrational number?That is to say, given two irrational numbers a and b, if a/b is a irrational number too, then for any m,n is nonzero integer, we have that the number ma+nb is a irrational number, why?
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Answers (1)

zlepljalz2
Answered 2022-07-02 Author has 22 answers
That's not true: Take a = 2 1, b = 2 . Then a b = 1 2 1 isn't rational, but a b = 1
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