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МатематикаВопрос:
54. $$2\sqrt{15}(\sqrt{5}-2\sqrt{3})(4\sqrt{45}-\frac{10}{\sqrt{5}})-\frac{4}{\sqrt{5}+\sqrt{3}}$$
Ответ:
54. Решим пример:
- $$2\sqrt{15}(\sqrt{5}-2\sqrt{3})(4\sqrt{45}-\frac{10}{\sqrt{5}})-\frac{4}{\sqrt{5}+\sqrt{3}} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(12\sqrt{5}-\frac{10}{\sqrt{5}})-\frac{4}{\sqrt{5}+\sqrt{3}} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(\frac{12 \cdot 5 - 10}{\sqrt{5}})-\frac{4}{\sqrt{5}+\sqrt{3}} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(\frac{60 - 10}{\sqrt{5}})-\frac{4}{\sqrt{5}+\sqrt{3}} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(\frac{50}{\sqrt{5}})-\frac{4(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(\frac{50\sqrt{5}}{5})-\frac{4(\sqrt{5}-\sqrt{3})}{5-3} = 2\sqrt{15}(\sqrt{5}-2\sqrt{3})(10\sqrt{5})-\frac{4(\sqrt{5}-\sqrt{3})}{2} = 100\sqrt{3} - 60\sqrt{5} - 2\sqrt{5} + 2\sqrt{3} = 102\sqrt{3} - 62\sqrt{5}$$
Ответ:$$102\sqrt{3} - 62\sqrt{5}$$
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