Question

Poate cineva sa ma ajute cu calculul asta (cu formula radicalilor compusi)​

Answer 1

$\sqrt{13 - 30 \sqrt{2 - \sqrt{9 - 4 \sqrt{2} } } } + \sqrt{13 + 30 \sqrt{2 + \sqrt{9 + 4 \sqrt{2} } } } \\ \\ = \sqrt{13 - 30 \sqrt{2 - \sqrt{(1 -2 \sqrt{2} ) {}^{2} } } } + \sqrt{13 + 30 \sqrt{2 + \sqrt{(1 + 2 \sqrt{2} ) {}^{2} } } } \\ \\ = \sqrt{13 - 30 \sqrt{2 - (2 \sqrt{2} - 1) } } + \sqrt{13 + 30 \sqrt{2 + 1 + 2 \sqrt{2} } } \\ \\ = \sqrt{13 - 30 \sqrt{(\sqrt{2} - 1) {}^{2} } } + \sqrt{13 + 30 \sqrt{( \sqrt{2} + 1) {}^{2} } } \\ \\ = \sqrt{13 - 30( \sqrt{2 } - 1)} + \sqrt{13 + 30( \sqrt{2 } + 1)} \\ \\ = \sqrt{13 - 30 \sqrt{2} + 30} + \sqrt{13 + 30 \sqrt{2} + 30 } \\ \\ = \sqrt{43 - 30 \sqrt{2} } + \sqrt{43 + 30 \sqrt{2} } \\ \\ = \sqrt{(5 - 3 \sqrt{2} ) {}^{2} } + \sqrt{(5 + 3 \sqrt{2} ) {}^{2} } \\ \\ = 5 - 3 \sqrt{2} + 5 + 3 \sqrt{2} \\ \\ = 5 + 5 \\ \\ = 10$