Вычислите с помощью формулы a^2-b^2=(a-b)(a+b): (5 1/6)^2-(7 1/3)^2.

\[\left( 5\frac{1}{6} \right)^{2} - \left( 7\frac{1}{3} \right)^{2} = \left( \frac{31}{6} \right)^{2} - \left( \frac{22}{3} \right)^{2} =\]

\[= \left( \frac{31}{6} \right)^{2} - \left( \frac{44}{6} \right)^{2} =\]

\[= \left( \frac{31}{6} - \frac{44}{6} \right)\left( \frac{31}{6} + \frac{44}{6} \right) =\]

\[= - \frac{7}{6} \cdot \frac{75}{6} = - \frac{7}{6} \cdot \frac{25}{2} =\]

\[= - \frac{175}{12} = - 14\frac{7}{12}.\]