(a) Consider the expression x - (x+a²)1/4 for x > 0 and a any real number. This expression suffers from cancellation. Find a mathematically equivalent but numerically more stable way to compute it. (b) A function f(x) is defined as follows: 1 f(x) = +3x-2. 4- x3 (b1) Show that the equation f(x) = 0 has a solution in (0, 1). (b2) To solve f(x) = 0, carry out one iteration from the initial point x0 = 1 with a method based on a first order approximation of f at a single point by a function g defined by g(x) = α + 4 - β x3 The parameters a and B are defined by the approximation conditions. Don't worry if your iterate does not land in (0, 1).