"""
0.05 = (x/(x+1))*raiz(6/(2+x))

f(x) = (x/(x+1))*raiz(6/(2+x)) - 0.05

"""
import math

def f(x):
    return (x/(x+1))*math.sqrt(6/(2+x))-0.05

def df(x):
    return (math.sqrt(6/(2+x)) - (x/(x+1))*(1/math.sqrt(6/(2+x))))/(x+1)**2

def newtonRaphson(x0, tol, n):
    print('\n\n*** Metodo de Newton-Raphson ***')
    i = 1
    while i <= n:
        x1 = x0 - f(x0)/df(x0)
        print('Iteracion-%d, x1 = %0.6f y f(x1) = %0.6f' % (i, x1, f(x1)))
        if abs(f(x1)) < tol:
            print('\nLa raiz es: %0.8f' % x1)
            return x1
        x0 = x1
        i = i + 1
    print('\nNo se encontro la raiz')
    return None

x0 = float(input('Ingrese el valor inicial: '))
tol = float(input('Ingrese la tolerancia: '))
n = int(input('Ingrese el numero maximo de iteraciones: '))
newtonRaphson(x0, tol, n)
print(f(0.02995472))