`x=-7\root{3}{49(5+4\sqrt{2})(3+2\sqrt{1+\sqrt{2}})(3-2\sqrt{1+\sqrt{2}})` `@` Tìm `x`

Đáp án + Giải thích các bước giải:

$x = -7\sqrt[3]{49(5 + 4\sqrt{2})(3 + 2\sqrt{1 + \sqrt{2}})(3 - 2\sqrt{1 + \sqrt{2}})}$ 

$= -7\sqrt[3]{49(5 + 4\sqrt{2})[9 - (2\sqrt{1 + \sqrt{2}})^2]}$

$= -7\sqrt[3]{49(5 + 4\sqrt{2})[9 - 4(1 + \sqrt{2})]}$

$= -7\sqrt[3]{49(5 + 4\sqrt{2})(9 - 4 - 4\sqrt{2})}$

$= -7\sqrt[3]{49(5 + 4\sqrt{2})(5 - 4\sqrt{2})}$

$= -7\sqrt[3]{49[25 - (4 \sqrt{2})^2]}$

$= -7\sqrt[3]{49(25 -32)}$
$= -7\sqrt[3]{49 . (-7)}$
$= -7\sqrt[3]{-343}$
$= -7 . (-7)$
$=49$