Approximate solution of equations
1. Solve the equation x3 + 50x – 60 = 0 to two decimal places.
Solution:
f(x) = x3 + 50x – 60
f/(x) = 3x2 + 50
2.Solve the equation x3 + x – 32 = 0 to two decimal places.
Solution:
f(x) = x3 + x – 32
f/(x)= 3x2 + 1
3.Solve the equation x3 + 2x – 8 = 0 to two decimal places.
Solution:
f(x) = x3 + 2x – 8
f/(x) = 3x2 + 2
4.Solve the equation 5x3 + 12x2 – 17x – 24 = 0 to two decimal places.
Solution:
f (x) = 5x3 + 12x2 – 17x – 24
f/(x) = 15x2 + 24x – 17
5.Solve the equation 2·ln x – x + 0.1·x2 = 0 to three decimal places.
Solution:
f (x) = 2·ln x – x + 0.1·x2
f/(x) = 2·x–1 – 1 + 0.2·x
