Use the given recursion and starting value of [tex]x_0 = 2.4[/tex] to find [tex]x_1[/tex] :
[tex]x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45[/tex]
Do the same for [tex]x_2[/tex] and [tex]x_3[/tex] :
[tex]x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949[/tex]
[tex]x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}[/tex]
(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)
