a.
\(B=\dfrac{x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)
\(P=\dfrac{A}{B}=\dfrac{\sqrt{x}+2}{\sqrt{x}}.\dfrac{\sqrt{x}-2}{\sqrt{x}}=\dfrac{x-4}{x}\)
b.
\(\left|B\right|=B\Leftrightarrow B\ge0\)
\(\Rightarrow\dfrac{\sqrt{x}}{\sqrt{x}-2}\ge0\)
\(\Leftrightarrow\sqrt{x}-2>0\) (do \(\sqrt{x}>0;\forall x>0\))
\(\Rightarrow x>4\)
c.
\(x.P\le10\sqrt{x}-29-\sqrt{x-25}\)
\(\Rightarrow x-4\le10\sqrt{x}-29-\sqrt{x-25}\)
\(\Leftrightarrow x-10\sqrt{x}+25\le-\sqrt{x-25}\)
\(\Leftrightarrow\left(\sqrt{x}-5\right)^2+\sqrt{x-25}\le0\) (1)
Do \(\left\{{}\begin{matrix}\left(\sqrt{x}-5\right)^2\ge0\\\sqrt{x-25}\ge0\end{matrix}\right.\) ; \(\forall x>0\)
\(\Rightarrow\left(\sqrt{x}-5\right)^2+\sqrt{x-25}\ge0\)
Nên (1) thỏa mãn khi và chỉ khi \(\left\{{}\begin{matrix}\left(\sqrt{x}-5\right)^2=0\\\sqrt{x-25}=0\end{matrix}\right.\)
\(\Rightarrow x=25\)
Anh chị giúp em với ạ^^
