Question

Solve the equation x² - 5 = √x - 2 by using successive approximation. Set the left-hand side of the equation equal to f(x) and the right-hand side equal to g(x): f(x) = x² - 5 and g(x) = √x - 2. Then answer the questions in the table.

The solution to the equation is:
a. x = 1
b. x = 2
c. x = 3
d. x = 4

Answer 1

To solve the equation x² - 5 = √x - 2 using successive approximation, set the left-hand side equal to f(x) and the right-hand side equal to g(x).

Step-by-step explanation:

To solve the equation x² - 5 = √x - 2 using successive approximation, we need to set the left-hand side of the equation equal to f(x) and the right-hand side equal to g(x). So, we have f(x) = x² - 5 and g(x) = √x - 2.

We can start by making an initial guess for x, let's say x = 2, and then substitute it into f(x) and g(x).

If the two values are not equal, we can refine our guess by substituting the new value of x back into the equations until we converge to a solution.

In this case, after performing successive approximations, we find that x = 4 is the solution to the equation.