Show that the equation x3+x2−10=0x^3 + x^2 - 10 = 0x3+x2−10=0 has a solution between x=1x = 1x=1 and x=2x = 2x=2.
Show that the equation x3+x2−10=0x^3 + x^2 - 10 = 0x3+x2−10=0 can be rearranged to give: x=10x+1\displaystyle x = \sqrt{\frac{10}{x + 1}}x=x+110
Starting with x0=2x_0 = 2x0=2, use the iteration formula xn+1=10xn+1\displaystyle x_{n+1} = \sqrt{\frac{10}{x_n + 1}}xn+1=xn+110 twice to find an estimate for the solution to x3+x2−10=0x^3 + x^2 - 10 = 0x3+x2−10=0.
