Show that the equation x3+5x−8=0x^3 + 5x - 8 = 0x3+5x−8=0 has a solution between x=1x = 1x=1 and x=2x = 2x=2.
Show that the equation x3+5x−8=0x^3 + 5x - 8 = 0x3+5x−8=0 can be rearranged to give: x=8x2+5\displaystyle x = \frac{8}{x^2 + 5}x=x2+58
Starting with x0=1x_0 = 1x0=1, use the iteration formula xn+1=8xn2+5\displaystyle x_{n+1} = \frac{8}{x_n^2 + 5}xn+1=xn2+58 twice to find an estimate for the solution to x3+5x−8=0x^3 + 5x - 8 = 0x3+5x−8=0.
