Question

Answer 1

4:

a: \(P=\left(\dfrac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\right):\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-x}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\dfrac{4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-4-x}\)

\(=\dfrac{4\sqrt{x}-4}{-4}=-\sqrt{x}+1\)

b: Khi x=3-2căn 2 thì \(P=-\left(\sqrt{2}-1\right)+1=-\sqrt{2}+1+1=2-\sqrt{2}\)

c: \(P\cdot\sqrt{x}=-x+\sqrt{x}\)

\(=-\left(x-\sqrt{x}+\dfrac{1}{4}\right)+\dfrac{1}{4}=-\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\)

Dấu = xảy ra khi x=1/4