suppose that x,y > 0 with x^{n} = y^{n}.
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/y^{n}, can you do this?).
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