Question

1. Cho biểu thức

P=\((\frac{2+\sqrt{x}}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}):\frac{4\sqrt{x}-4}{x-2\sqrt{x}}\)

Với x>0, x≠1, x≠4

a, Rút gọn

b, Tính P khi x= \(3+2\sqrt{2}\)

c, Tìm x để P=\(\frac{1}{2}\)

Answer 1

a/ \(P=\left(\frac{\left(2+\sqrt{x}\right)\left(\sqrt{x}-2\right)-x}{\sqrt{x}\left(\sqrt{x}-2\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{4\left(\sqrt{x}-1\right)}\)

\(P=\frac{x-4-x}{4\sqrt{x}-4}=\frac{-1}{\sqrt{x}-1}\)

b/ Thay x=\(3+2\sqrt{2}\) vào P có:

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

c/ \(P=\frac{1}{2}\Leftrightarrow\frac{-1}{\sqrt{x}-1}=\frac{1}{2}\Leftrightarrow-2=\sqrt{x}-1\Leftrightarrow\sqrt{x}=-1\left(vl\right)\)

Vậy ko tồn tai x để P=1/2