Thread: Rational numbers

If z is a real number, then is defined recursively for non-negative integers



And, for

.

If z is a positive real number, and b a natural number, then we may define the positive bth root

to be the positive real number y such that

.

You may assume that a positive real number always has a positive bth root.

a) Given a positive real number z, is it possible for there to be two different positive bth roots of z? Justify your answer briefly.

Any help would be greatly appreciated

suppose that x,y > 0 with xⁿ = yⁿ.

show if x/y > 1, then (x/y)ⁿ > 1, and similarly if x/y < 1

(you might need to prove first that (1/y)ⁿ = 1/yⁿ, can you do this?).