Điều kiện x \ge 0. BPT
\Leftrightarrow 4x^2-1+\sqrt{3x}-\sqrt{x+1} \le 0
\Leftrightarrow (2x-1)(2x+1)+\frac{2x-1}{\sqrt{3x}+\sqrt{x+1} }\le 0
\Leftrightarrow (2x-1)\left ( 2x+1+\frac{1}{\sqrt{3x}+\sqrt{x+1} } \right )\le 0
Do x\ge 0 \Rightarrow 2x+1+\frac{1}{\sqrt{3x}+\sqrt{x+1} }>0 nên BPT
\Leftrightarrow 2x-1 \le 0 \Leftrightarrow x \le 1/2.