Question

Преобразуй в произведение ∛ + 2cos π/8

Answer 1

Ответ:

$\sqrt[3]{2cos\dfrac{\pi}{8}}=\sqrt[3]{2\cdot \sqrt{\dfrac{1+cos\frac{\pi}{4}}{2}}}=\sqrt[3]{\sqrt{2\cdot (1+cos\dfrac{\pi}{4}})}=\sqrt[6]{2\cdot (1+\dfrac{\sqrt2}{2})}=\\\\\\=\sqrt[6]{2+\sqrt2}=\sqrt[6]{\sqrt2\cdot (1+\sqrt2)}}=\sqrt[12]{2}\cdot \sqrt[6]{1+\sqrt2}$