Question

Rút gọn hoặc tính giá trị biểu thức:

1.\(\sqrt{m+2\sqrt{m-1}}-\sqrt{m-2\sqrt{m-1}}\)

2.\(\sqrt{2x+2\sqrt{x^2}-1}với\hept{\begin{cases}x\ge1\\\sqrt{x-1}+\sqrt{x+1}=\sqrt{7}\end{cases}}\)

3.\(\frac{\sqrt{4m^2+12m+9}}{2m+1}\) tại  \(m=-1\frac{1}{2}\)

4.\(\frac{\sqrt{3}\left(x-1\right)}{\sqrt{x^2-x+1}}\) tại \(x=2+\sqrt{3}\)

Answer 1

#)Giải :

1.\(\sqrt{m+2\sqrt{m-1}}-\sqrt{m-2\sqrt{m-1}}\)

\(=\sqrt{m-1+2\sqrt{m-1}+1}+\sqrt{m-1-2\sqrt{m-1}+1}\)

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

\(=\sqrt{m-1}+1+\sqrt{m-1}-1\)

\(=2\sqrt{m-1}\)