Question

Answer 1

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

\(P=\dfrac{2x+2-3\sqrt{x}-1}{x-1}\)

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

\(P=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}\)

b) Để P<1 

\(2\sqrt{x}-1< \sqrt{x}+1\)

\(\sqrt{x}< 2\)

\(x< 4\)

Vậy \(0\le x< 4\), \(x\ne1\)