SOLUTION: plz give this soluation...
if √( x+(1/x)) is a irrational number then how can i prove that?
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Question 1001489: plz give this soluation...
if √( x+(1/x)) is a irrational number then how can i prove that?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
I just posted one possibility...
Prove is irrational.
If the radicand is not a perfect square, then the root must be irrational.
We can rewrite the radicand as
x + 1/x = (x+1)/x
The only way (x+1)/x can be a perfect square is if x+1 and x are both perfect squares...
If x is a perfect square, then x+1 cannot be.
If x+1 is a perfect square, then x cannot be.
Thus is irrational.
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