Question

Answer 1

a: \(M=\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\frac{x-4\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}\cdot\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-2}{\sqrt{x}}\)

b: Thay \(x=3+2\sqrt2=\left(\sqrt2+1\right)^2\) vào M, ta được:

\(M=\frac{\sqrt{\left(\sqrt2+1\right)^2}-2}{\sqrt{\left(\sqrt2+1\right)^2}}=\frac{\sqrt2+1-2}{\sqrt2+1}=\frac{\sqrt2-1}{\sqrt2+1}=\left(\sqrt2-1\right)^2=3-2\sqrt2\)

c: M>0

=>\(\frac{\sqrt{x}-2}{\sqrt{x}}>0\)

=>\(\sqrt{x}-2>0\)

=>\(\sqrt{x}>2\)

=>x>4