Question

The function f(x) = g(x), where f(x) = 2x – 5 and g(x) = x2 – 6.

The table below shows the process of solving using successive approximations:
Continue this process to find the positive solution to the nearest 10th

Answer 1

`x=2.4`

Explanation:

Solving Equations Using Successive Approximations

We need to find the solution to the equation

`f(x)=g(x)`

where

`f(x)=2x-5`

`g(x)=x^2-6`

The approximation has been already started and reached a state for x=2.5 where

`f(2.5)=0`

`g(2.5)=2.5^2-6=0.25`

The difference between the results is 0.25, we need further steps to reach a good solution (to the nearest tenth)

Let's test for x=2.4

`f(2.4)=-0.2`

`g(2.4)=2.4^2-6=-0.24`

The new difference is -0.2+0.24=0.04

It's accurate enough, thus the solution is

`\boxed{x=2.4}`