ĐKXĐ: \(x\ge1\)
\(\Leftrightarrow x^2-4+1-\sqrt{x-1}+2-\sqrt{3x-2}=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)-\frac{x-2}{\sqrt{x-1}+1}-\frac{3\left(x-2\right)}{\sqrt{3x-2}+2}=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2-\frac{1}{\sqrt{x-1}+1}-\frac{3}{\sqrt{3x-2}+2}\right)=0\)
Do \(x\ge1\Rightarrow\left\{{}\begin{matrix}x+2\ge3\\\frac{1}{\sqrt{x-1}+1}\le1\\\frac{3}{\sqrt{3x-2}+2}\le1\end{matrix}\right.\) \(\Rightarrow\) ngoặc phía sau luôn dương
Vậy p có nghiệm duy nhất \(x=2\)