Question

Let F(x) = 1/sqrt(x+1). Sketch carefully the graph of y = F(x) for 0 <= x <= 2. Add the line y = x to your diagram, and indicate the location of the root r of the equation F(x) = x. use algebra to show that x = r also solves the equation x^3 + x^2 = 1. Use the method of simple iteration to calculate r to 5 significant figures.

Need help with using x=r to solve x^3 + x^2 = 1.

Answer 1

the process is tedious but here goes
pick x0= 1 => 1^3 +1^2 =1 => 2 = 1, thats to large,
pick x1 = .5 => 0.375=1 ,thats too small
pick x2 = .75=> 0.984375=1 , still a bit small
pick x3 = .755 =>1.000393875=1 , a bit large
pick x4 = .7545=> 0.99878465=1, a bit small
pick x5 = .7548=>0.99974999=1, a bit small
pick x6= .75488=> 1.0000075=1 correct to 5 sigdigs

Answer 2

you might have to take midpoints each time aswell i didnt tho