rut gon sqrt(4-sqrt7)-sqrt(4+sqrt7)

CHÚC BẠN HỌC TỐT !!!!!!!

Đáp án:

$- \sqrt{2}$

Giải thích các bước giải:

     $\sqrt{4 - \sqrt{7}} - \sqrt{4 + \sqrt{7}}$

$= \dfrac{1}{\sqrt{2}}.\sqrt{2}(\sqrt{4 - \sqrt{7}} - \sqrt{4 + \sqrt{7}})$

$= \dfrac{1}{\sqrt{2}}.[\sqrt{2(4 - \sqrt{7})} - \sqrt{2(4 + \sqrt{7})}]$

$= \dfrac{1}{\sqrt{2}}.(\sqrt{8 - 2\sqrt{7}} - \sqrt{8 + 2\sqrt{7}})$

$= \dfrac{1}{\sqrt{2}}.(\sqrt{7 - 2\sqrt{7} + 1} - \sqrt{7 + 2\sqrt{7} + 1})$

$= \dfrac{1}{\sqrt{2}}.[\sqrt{(\sqrt{7} - 1)^2} - \sqrt{(\sqrt{7} + 1)^2}]$

$= \dfrac{1}{\sqrt{2}}.(|\sqrt{7} - 1| - |\sqrt{7} + 1|)$

$= \dfrac{1}{\sqrt{2}}.(\sqrt{7} - 1 - \sqrt{7} - 1)$

$= \dfrac{1}{\sqrt{2}}.(- 2)$

$= - \sqrt{2}$