Question

You are using Newton's method to solve x3-5x-2=0. If your first guess is x1=2, what value will you calculate for the next approximation x2?

Answer 1

your equation would be

xnew = x - (x^3 - 5x - 2)/(3x^2 - 5)

so for x=2
xnew = 2 - (8-10-2)/(12-5)
= 2.5714

Incidentally, my next 4 answers were

2.4268029
2.4143045
2.4142136 and
2.4142136 which would be one of the answers correct up to 7 decimal places.

Answer 2

90+89=