Question

Answer 1

1: ĐKXĐ: x>=0; x<>1

2: \(M=\dfrac{x-\sqrt{x}-2-\left(x+\sqrt{x}-2\right)}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}-1}{2}\cdot\left(\sqrt{x}-1\right)\)

\(=\dfrac{x-\sqrt{x}-2-x-\sqrt{x}+2}{2}\cdot\left(\sqrt{x}-1\right)\)

\(=\dfrac{-2\sqrt{x}}{2}\cdot\left(\sqrt{x}-1\right)=-\sqrt{x}\left(\sqrt{x}-1\right)\)

3: \(M-\dfrac{1}{4}=-x+\sqrt{x}-\dfrac{1}{4}=-\left(\sqrt{x}-\dfrac{1}{2}\right)^2< =0\)

Do đó: M<=1/4