Question

cho mình hỏi bài này

Answer 1

\(B=\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\)

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

Answer 2

B=\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

=>\(B^2=4-\sqrt{7}+4+\sqrt{7}-2\sqrt{\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)}=8-2\sqrt{16-7}\)

\(B^2=8-2\sqrt{9}=8-2.3=8-6=2\)

\(\Rightarrow B=\sqrt{2}\) hoặc \(B=-\sqrt{2}\)

Vì \(4-\sqrt{7}< 4+\sqrt{7}\Rightarrow\sqrt{4-\sqrt{7}}< \sqrt{4+\sqrt{7}}\)

\(\Leftrightarrow\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}< 0\)

hay B<0=>B=\(-\sqrt{2}\)