Chọn dấu "<", ">", "=" thích hợp cho ô trống: 5/6 - (1/6)^2 ? (5/6 - 1/6)^2

Lời giải:

Ta có: \(\frac{5}{6} - {\left( {\frac{1}{6}} \right)^2} = \frac{5}{6} - \frac{1}{{36}} = \frac{{30}}{{36}} - \frac{1}{{36}} = \frac{{29}}{{36}}\);

\({\left( {\frac{5}{6} - \frac{1}{6}} \right)^2} = {\left( {\frac{2}{3}} \right)^2} = \frac{4}{9} = \frac{{16}}{{36}}\).

Vì 29 > 16 nên \(\frac{{29}}{{36}} > \frac{{16}}{{36}}\) hay \(\frac{5}{6} - {\left( {\frac{1}{6}} \right)^2} > {\left( {\frac{5}{6} - \frac{1}{6}} \right)^2}\)

Vậy $\frac{5}{6}-{\left(\frac{1}{6}\right)}^2$ > ${\left(\frac{5}{6}-\frac{1}{6}\right)}^2$