Intermediate Value Theorem proof

[Anisotropic Galaxy]

Hi, can someone please help me here?

Prove that every nonnegative real number x has a unique nonnegative nth root x^(1/n).

The problem gives a hint - existence of x^(1/n) can be seen by applying intermediate value theorem to function f(t) = t^n for t>= 0.

But I still don't get it - proofs are such a hurdle for me. I'm hoping that I can get over that hurdle...soon...

Thanks!

 

[ComputerGeek]

Hi, can someone please help me here?
Prove that every nonnegative real number x has a unique nonnegative nth root x^(1/n).
The problem gives a hint - existence of x^(1/n) can be seen by applying intermediate value theorem to function f(t) = t^n for t>= 0.
But I still don't get it - proofs are such a hurdle for me. I'm hoping that I can get over that hurdle...soon...
Thanks!

try to get a contradiction of the statement you want to prove. so, assume that there exists two non negative real which have the same root. then you should be able to use the IVT to show that the two real numbers are actually the same number and that is a contradiction of your assumption which proves the proof statement.