Question

Chứng minh :

a) 8 - 2\(\sqrt{7}\) = ( \(\sqrt{7}-1\) )²

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

Answer 1

a) Ta có: \(VT=8-2\sqrt{7}\)

\(=7-2\cdot\sqrt{7}\cdot1+1\)

\(=\left(\sqrt{7}-1\right)^2\)

=VP(đpcm)

b) Ta có: \(VT=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{7-2\cdot\sqrt{7}\cdot1+1}-\sqrt{7+2\cdot\sqrt{7}\cdot1+1}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|\)

\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\)

\(=\sqrt{7}-1-\sqrt{7}-1=-2=VP\)(đpcm)