Qual a maior raiz da equação $x^2 - (2,333\dots)x + (1,333\dots) = 0$?

$2,333\dots = \dfrac{7}{3}$

 

$1,333\dots = \dfrac{4}{3}$

$\Delta = \left(-\dfrac{7}{3}\right)^2 - \dfrac{16}{3} = \dfrac{49}{9} - \dfrac{48}{9} = \dfrac{1}{9}$

 

$x = \dfrac{\dfrac{7}{3} \pm \dfrac{1}{3}}{2}$

$x = \dfrac{4}{3}\ \vee\ x = 1$

Logo a maior raiz é $\fbox{$\dfrac{4}{3}$}$.