Lời giải:
a. Khi $x=25$ thì $B=\frac{1}{\sqrt{25}-2}=\frac{1}{5-2}=\frac{1}{3}$
b. \(A=\frac{x+2}{(\sqrt{x}+1)(\sqrt{x}-2)}-\frac{2\sqrt{x}(\sqrt{x}-2)}{(\sqrt{x}+1)(\sqrt{x}-2)}+\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{(\sqrt{x}-2)(\sqrt{x}+1)}\)
\(=\frac{x+2-2x+4\sqrt{x}+x-1}{(\sqrt{x}+1)(\sqrt{x}-2)}=\frac{4\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}\)
\(\Rightarrow P=A:B=\frac{4\sqrt{x}+1}{\sqrt{x}+1}\)
Từ đây suy ra $P>0$
c.
\(P^2=P+2\Leftrightarrow P^2-P-2=0\Leftrightarrow (P+1)(P-2)=0\)
$\Leftrightarrow P=2$ (do $P>0$)
$\Leftrightarrow \frac{4\sqrt{x}+1}{\sqrt{x}+1}=2$
$\Leftrightarrow 4\sqrt{x}+1=2\sqrt{x}+2$
$\Leftrightarrow 2\sqrt{x}=1\Leftrightarrow x=\frac{1}{4}$ (tm)
