✔ 最佳答案
We use the Newton's method to find the approximate root as follows:
Let f(x) = (1 + x)5 - 15x, then we have:
f(0) = 1 and f(1) = -15
Thus, we are sure that there's a root between x = 0 and x = 1
Also f'(x) = 5(1 + x)4 - 15
Starting from x0 = 0:
x1 = x0 - f(x0)/f'(x0) = 0.1
x2 = x1 - f(x1)/f'(x1) = 0.11439
x3 = x2 - f(x2)/f'(x2) = 0.11477
x4 = x3 - f(x3)/f'(x3) = 0.11477
Thus, correcting to 5 d.p., we can approximate x = 0.11477