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yanasochi
@yanasochi
July 2022
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Пожалуйста помогите хотябы 3 первых задания!!!!! Даю 100 баллов!!!!!
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Answers & Comments
1)![\frac{2}{5}\sqrt{75} + \sqrt{2}( \sqrt{2} - \sqrt{6} ) = 2\sqrt{3} + 2 -\sqrt{12} = 2 + 2\sqrt{3} - 2\sqrt{3} = 2 \frac{2}{5}\sqrt{75} + \sqrt{2}( \sqrt{2} - \sqrt{6} ) = 2\sqrt{3} + 2 -\sqrt{12} = 2 + 2\sqrt{3} - 2\sqrt{3} = 2](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%5Csqrt%7B75%7D%20%2B%20%20%5Csqrt%7B2%7D%28%20%5Csqrt%7B2%7D%20-%20%5Csqrt%7B6%7D%20%20%29%20%3D%202%5Csqrt%7B3%7D%20%20%2B%202%20-%5Csqrt%7B12%7D%20%3D%202%20%2B%202%5Csqrt%7B3%7D%20-%202%5Csqrt%7B3%7D%20%3D%202)
2) a)![\frac{\sqrt{a} + 7 }{49 - a} = \frac{\sqrt{a} + 7 }{7^{2} - \sqrt{a}^{2} } = \frac{\sqrt{a} + 7 }{(7 - \sqrt{a} )(\sqrt{a} + 7 )} } = \frac{1}{7-\sqrt{a} } \frac{\sqrt{a} + 7 }{49 - a} = \frac{\sqrt{a} + 7 }{7^{2} - \sqrt{a}^{2} } = \frac{\sqrt{a} + 7 }{(7 - \sqrt{a} )(\sqrt{a} + 7 )} } = \frac{1}{7-\sqrt{a} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Ba%7D%20%2B%207%20%7D%7B49%20-%20a%7D%20%3D%20%20%5Cfrac%7B%5Csqrt%7Ba%7D%20%2B%207%20%7D%7B7%5E%7B2%7D%20%20-%20%5Csqrt%7Ba%7D%5E%7B2%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%7Ba%7D%20%2B%207%20%7D%7B%287%20-%20%5Csqrt%7Ba%7D%20%29%28%5Csqrt%7Ba%7D%20%2B%207%20%29%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B7-%5Csqrt%7Ba%7D%20%7D)
б)![\frac{2 + \sqrt{2} }{\sqrt{10} + \sqrt{5} } = \frac{\sqrt{2}(\sqrt{2} + 1)}{\sqrt{5}(\sqrt{2} + 1 )} = \sqrt{\frac{2}{5} } = \sqrt{\frac{4}{10} } = \frac{2}{\sqrt{10} } \frac{2 + \sqrt{2} }{\sqrt{10} + \sqrt{5} } = \frac{\sqrt{2}(\sqrt{2} + 1)}{\sqrt{5}(\sqrt{2} + 1 )} = \sqrt{\frac{2}{5} } = \sqrt{\frac{4}{10} } = \frac{2}{\sqrt{10} }](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%2B%20%5Csqrt%7B2%7D%20%7D%7B%5Csqrt%7B10%7D%20%2B%20%5Csqrt%7B5%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B2%7D%28%5Csqrt%7B2%7D%20%2B%201%29%7D%7B%5Csqrt%7B5%7D%28%5Csqrt%7B2%7D%20%2B%201%20%29%7D%20%20%3D%20%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%20%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B4%7D%7B10%7D%20%7D%20%3D%20%5Cfrac%7B2%7D%7B%5Csqrt%7B10%7D%20%7D)
3) a)![\frac{63}{\sqrt{7} } = \frac{\sqrt{63} }{\sqrt{49}} = \sqrt{\frac{7*9}{7} } = 3 \frac{63}{\sqrt{7} } = \frac{\sqrt{63} }{\sqrt{49}} = \sqrt{\frac{7*9}{7} } = 3](https://tex.z-dn.net/?f=%5Cfrac%7B63%7D%7B%5Csqrt%7B7%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B63%7D%20%7D%7B%5Csqrt%7B49%7D%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B7%2A9%7D%7B7%7D%20%7D%20%3D%203)
б)![\frac{3}{\sqrt{15} + \sqrt{6} }} = \frac{3(\sqrt{15} - \sqrt{6} )}{15 - 6} = \frac{3(\sqrt{15} - \sqrt{6} )}{9} = \frac{(\sqrt{15} - \sqrt{6} )}{3} \frac{3}{\sqrt{15} + \sqrt{6} }} = \frac{3(\sqrt{15} - \sqrt{6} )}{15 - 6} = \frac{3(\sqrt{15} - \sqrt{6} )}{9} = \frac{(\sqrt{15} - \sqrt{6} )}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B%5Csqrt%7B15%7D%20%2B%20%5Csqrt%7B6%7D%20%7D%7D%20%3D%20%5Cfrac%7B3%28%5Csqrt%7B15%7D%20-%20%5Csqrt%7B6%7D%20%20%29%7D%7B15%20-%206%7D%20%3D%20%5Cfrac%7B3%28%5Csqrt%7B15%7D%20-%20%5Csqrt%7B6%7D%20%20%29%7D%7B9%7D%20%3D%20%5Cfrac%7B%28%5Csqrt%7B15%7D%20-%20%5Csqrt%7B6%7D%20%20%29%7D%7B3%7D)