c) Cho P= A.B . So sánh P với 2

c) Ta có: $P=A.B=\frac{x+\sqrt{x}+1}{\sqrt{x}-4}.\frac{\sqrt{x}-4}{\sqrt{x}}=\frac{x+\sqrt{x}+1}{\sqrt{x}}$ 

Xét $P-2=\frac{x+\sqrt{x}+1}{\sqrt{x}}-2=\frac{x-\sqrt{x}+1}{\sqrt{x}}=\frac{{\left(\sqrt{x}-\frac{1}{2}\right)}^2+\frac{3}{4}}{\sqrt{x}}>0,\forall x>0$ 

Vậy P > 0 với $x>0,x\ne 4,x\ne 16$.