Question

Докажите тождество пожалуйста

Answer 1

$\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}} =\sqrt[3]{8+12\sqrt{2}+12+2\sqrt{2}} +\sqrt[3]{-12\sqrt{2}+12-2\sqrt{2}}=\\\\=\sqrt[3]{(2+\sqrt{2})^{3}}+\sqrt[3]{(2-\sqrt{2})^{3}} =2+\sqrt{2}+2-\sqrt{2} =4\\\\4=4$