Bài 4:
a. ĐKXĐ: \(\left\{\begin{matrix} x-1\geq 0\\ x-1\neq 2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq 1\\ x\neq 3\end{matrix}\right.\)
b. \(B=\frac{x-3}{\frac{x-1-2}{\sqrt{x-1}+\sqrt{2}}}=\sqrt{x-1}+\sqrt{2}\)
\(x=4(2-\sqrt{3})\Rightarrow x-1=7-4\sqrt{3}=(2-\sqrt{3})^2\)
\(\Rightarrow \sqrt{x-1}=2-\sqrt{3}\Rightarrow B=\sqrt{x-1}+\sqrt{2}=2-\sqrt{3}+\sqrt{2}\)
c.
$\sqrt{x-1}\geq 0$ với mọi $x\geq 1; x\neq 3$
$\Rightarrow B=\sqrt{x-1}+\sqrt{2}\geq \sqrt{2}$
Vậy $B_{\min}=\sqrt{2}$ khi $x=1$
Bài 5:
\(C=\frac{x-2\sqrt{xy}+y+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{xy}(\sqrt{x}-\sqrt{y})}{\sqrt{xy}}\)
\(=\frac{(\sqrt{x}+\sqrt{y})^2}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})=(\sqrt{x}+\sqrt{y})-(\sqrt{x}-\sqrt{y})\)
\(=2\sqrt{y}\) vẫn phụ thuộc vào biến $y$ bạn ạ. Bạn xem lại đề.
Bài 6:
a. ĐKXĐ: $x\geq 0; x\neq 4$
\(D=\left[\frac{\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}-\frac{2(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}+2)}+\frac{\sqrt{x}-2}{(\sqrt{x}+2)(\sqrt{x}-2)}\right]:\frac{(\sqrt{x}+2)(\sqrt{x}-2)+10-x}{\sqrt{x}+2}\)
\(=\frac{-6}{(\sqrt{x}-2)(\sqrt{x}+2)}:\frac{6}{\sqrt{x}+2}=\frac{-6}{(\sqrt{x}-2)(\sqrt{x}+2)}.\frac{\sqrt{x}+2}{6}=\frac{1}{2-\sqrt{x}}\)
b.
Để $D>0\Leftrightarrow \frac{1}{2-\sqrt{x}}>0$
$\Leftrightarrow 2-\sqrt{x}>0$
$\Leftrightarrow 2>\sqrt{x}$
$\Leftrightarrow 0\leq x< 4$
Kết hợp với đkxđ suy ra $0\leq x< 4$
