điều kiện xác định : \(x\ge1\)
ta có : \(P=x-\sqrt{x-1}+1=x-1-\sqrt{x-1}+\dfrac{1}{4}+\dfrac{7}{4}\)
\(=\left(\sqrt{x-1}-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)
\(\Rightarrow P_{min}=\dfrac{7}{4}\) khi \(x=\dfrac{5}{4}\)
vậy ...........................................................................................................................