Question

Rút gọn

A=\(\dfrac{\sqrt{\sqrt{7}-\sqrt{3}-}-\sqrt{\sqrt{7}+\sqrt{3}}}{\sqrt{\sqrt{7}-2}}\)

Answer 1

Ta có : \(\sqrt{\sqrt{7}-2}>0\)

\(\sqrt{\sqrt{7}-3}< \sqrt{\sqrt{7}+3}\Rightarrow\sqrt{\sqrt{7}-3}-\sqrt{\sqrt{7}+3}< 0\)=> A < 0

Xét \(A^2=\dfrac{\sqrt{7}-3+\sqrt{7}+3-2\sqrt{\left(\sqrt{7}-3\right)\left(\sqrt{\sqrt{7}+3}\right)}}{\sqrt{7}-2}\)

= \(\dfrac{2\sqrt{7}-2\sqrt{4}}{\sqrt{7}-2}=\dfrac{2\sqrt{7}-4}{\sqrt{7}-2}=\dfrac{2\left(\sqrt{7}-2\right)}{\sqrt{7}-2}=2\)

Answer 2

Thiếu xíu cho bổ sung (tiếp):

A² = 2 , A < 0 => A = \(-\sqrt{2}\)