Answer:
[tex]x=2.4[/tex]
Step-by-step explanation:
Solving Equations Using Successive Approximations
We need to find the solution to the equation
[tex]f(x)=g(x)[/tex]
where
[tex]f(x)=2x-5[/tex]
[tex]g(x)=x^2-6[/tex]
The approximation has been already started and reached a state for x=2.5 where
[tex]f(2.5)=0[/tex]
[tex]g(2.5)=2.5^2-6=0.25[/tex]
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
[tex]f(2.4)=-0.2[/tex]
[tex]g(2.4)=2.4^2-6=-0.24[/tex]
The new difference is -0.2+0.24=0.04
It's accurate enough, thus the solution is
[tex]\boxed{x=2.4}[/tex]
