Решебник по алгебре 9 класс Мерзляк Задание 87

\[\boxed{\text{87\ (87).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \sqrt{6} + \sqrt{3}\ и\ \sqrt{7} + \sqrt{2}\]

\[\left( \sqrt{6} + \sqrt{3} \right)^{2} = 6 + 3 + 2\sqrt{18} =\]

\[= 9 + \sqrt{72}\]

\[\left( \sqrt{7} + \sqrt{2} \right)^{2} = 7 + 2 + 2\sqrt{14} =\]

\[= 9 + \sqrt{56}\]

\[\sqrt{72} > \sqrt{56}:\]

\[\sqrt{6} + \sqrt{3} > \sqrt{7} + \sqrt{2}.\]

\[2)\ \sqrt{26} - \sqrt{2}\ \ \ и\ \ \sqrt{14}\]

\[\left( \sqrt{26} - \sqrt{2} \right)^{2} = 26 + 2 -\]

\[- 2\sqrt{52} = 28 - 4\sqrt{13}\]

\[\left( \sqrt{14} \right)^{2} = 14\]

\[25 - 4\sqrt{13}\ и\ 14\]

\[28 - 14\ и\ 4\sqrt{13}\]

\[14\ V\ 4\sqrt{13}\ \ \ \ \ \ \ \ \ |\ :2\]

\[(7)^{2\ }\ и\ \left( 2\sqrt{13} \right)^{2}\]

\[49 < 52:\]

\[\sqrt{26} - \sqrt{2} < \sqrt{14}.\]