Докажите, что:
$\sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{3}}}} * \sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{3}}}} = 1$.
$\sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{3}}}} * \sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{3}}}} = \sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{2^2 - (\sqrt{2 + \sqrt{2 + \sqrt{3}}})^2} = \sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{4 - (2 + \sqrt{2 + \sqrt{3}})} = \sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{4 - 2 - \sqrt{2 + \sqrt{3}}} = \sqrt{2 + \sqrt{3}} * \sqrt{2 + \sqrt{2 + \sqrt{3}}} * \sqrt{2 - \sqrt{2 + \sqrt{3}}} = \sqrt{2 + \sqrt{3}} * \sqrt{(2 + \sqrt{2 + \sqrt{3}})(2 - \sqrt{2 + \sqrt{3}})} = \sqrt{2 + \sqrt{3}} * \sqrt{2^2 - (2 + \sqrt{3})} = \sqrt{2 + \sqrt{3}} * \sqrt{4 - 2 - \sqrt{3}} = \sqrt{2 + \sqrt{3}} * \sqrt{2 - \sqrt{3}} = \sqrt{(2 + \sqrt{3})(2 - \sqrt{3})} = \sqrt{2^2 - (\sqrt{3})^2} = \sqrt{4 - 3} = \sqrt{1} = 1$
Пожауйста, оцените решение
