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МатематикаВопрос:
47. $$4\sqrt{15}-\frac{\sqrt{27}}{2\sqrt{3}-\sqrt{5}}$$
Ответ:
47. Решим пример:
- $$4\sqrt{15}-\frac{\sqrt{27}}{2\sqrt{3}-\sqrt{5}} = 4\sqrt{15} - \frac{3\sqrt{3}}{2\sqrt{3}-\sqrt{5}} = 4\sqrt{15} - \frac{3\sqrt{3}(2\sqrt{3}+\sqrt{5})}{(2\sqrt{3}-\sqrt{5})(2\sqrt{3}+\sqrt{5})} = 4\sqrt{15} - \frac{3\sqrt{3}(2\sqrt{3}+\sqrt{5})}{12-5} = 4\sqrt{15} - \frac{3\sqrt{3}(2\sqrt{3}+\sqrt{5})}{7} = 4\sqrt{15} - \frac{18 + 3\sqrt{15}}{7} = \frac{28\sqrt{15} - 18 - 3\sqrt{15}}{7} = \frac{25\sqrt{15}-18}{7}$$
Ответ:$$\frac{25\sqrt{15}-18}{7}$$
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