a. On the same axes, sketch the graphs of y = √x and y = 2/3.

b. With reference to your sketch, explain why the equation √x = 2/x has exactly one real root.

c. Given that f(x) = √x − 2/x , show that the equation f(x) = 0 has a root r, where 1 < r < 2.

d. Show that the equation √x = 2/x may be written in the form x^p = q, where p and q are integers to be found.

e. Hence write down the exact value of the root of the equation √x − 2/x = 0.