57. $$-3\sqrt{15}-4(\frac{\sqrt{48}}{6+\sqrt{60}})^{2}+(\frac{8}{\sqrt{32}})^{2}$$

57. Решим пример:

• $$-3\sqrt{15}-4(\frac{\sqrt{48}}{6+\sqrt{60}})^{2}+(\frac{8}{\sqrt{32}})^{2} = -3\sqrt{15}-4(\frac{4\sqrt{3}}{6+2\sqrt{15}})^{2}+(\frac{8}{4\sqrt{2}})^{2} = -3\sqrt{15}-4(\frac{2\sqrt{3}}{3+\sqrt{15}})^{2}+(\frac{2}{\sqrt{2}})^{2} = -3\sqrt{15}-4(\frac{12}{9+6\sqrt{15}+15})+2 = -3\sqrt{15}-4(\frac{12}{24+6\sqrt{15}})+2 = -3\sqrt{15}-4(\frac{2}{4+\sqrt{15}})+2 = -3\sqrt{15}-\frac{8}{4+\sqrt{15}}+2 = -3\sqrt{15}-\frac{8(4-\sqrt{15})}{(4+\sqrt{15})(4-\sqrt{15})}+2 = -3\sqrt{15}-\frac{32 - 8\sqrt{15}}{16-15}+2 = -3\sqrt{15}-32 + 8\sqrt{15}+2 = 5\sqrt{15}-30$$

Ответ:$$5\sqrt{15}-30$$