Hey can you guys help me out with this problem:
It is given that is rational, where a,b,c and d are positive integers and c is not a square. Show that as a consequence, . Use this result to show that is not rational.
Never mind about that second part, my math teacher has solved it. Thank you very much Soroban.
For those who want to know the solution:
The first fraction that was given when compared to the second fraction: it can be seen that b = 1. Now for it to be true, the above proven equation has to hold.
When you sub b=1 into the proven equation above, it can be seen that
However, as a, c and d are positive integers, that fraction has to be less than one, and hence this is impossible because c is a positive integer.
Therefore, the second fraction is never rational.
PS. By fraction I mean everything that is need to be proved irrational and everything that is need to be proved irrational.