Question

Chứng Minh

\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)

Answer 1

Ta có:  \(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

\(=\sqrt{5-4\sqrt{5}+4}-\sqrt{5}\)

\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\)

\(=|\sqrt{5}-2|-\sqrt{5}\)

\(=\sqrt{5}-2-\sqrt{5}\)

\(=-2\)= VP

=> đpcm

=.= hok tốt!!

Answer 2

\(VT=\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

\(=\sqrt{4-4\sqrt{5}+5}-\sqrt{5}\)

\(=\sqrt{\left(2-\sqrt{5}\right)^2}-\sqrt{5}\)

\(=\left|2-\sqrt{5}\right|-\sqrt{5}\)

\(=\sqrt{5}-2-\sqrt{5}\)

\(=-2\)

\(=VP\)

Vậy đẳng thức được chứng minh