\(A=\dfrac{1}{3}\sqrt{5.3^2}-\sqrt{2^2.5}+\sqrt{\left(2+\sqrt{5}\right)^2}\)
\(=\sqrt{5}-2\sqrt{5}+2+\sqrt{5}\)
\(=2\)
\(B=\dfrac{\sqrt{x}.\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{2\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{x-2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}}\)
\(A=3B\Leftrightarrow2=\dfrac{3\sqrt{x}-3}{\sqrt{x}}\Rightarrow2\sqrt{x}=3\sqrt{x}-3\)
\(\Rightarrow\sqrt{x}=3\Rightarrow x=9\)
Lời giải:
a.
\(A=\frac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}=\frac{1}{3}\sqrt{3^2.5}-\sqrt{2^2.5}+\sqrt{(\sqrt{5}+2)^2}\)
\(=\frac{1}{3}.3\sqrt{5}-2\sqrt{5}+\sqrt{5}+2=\sqrt{5}-2\sqrt{5}+\sqrt{5}+2=2\)
\(B=\frac{x}{\sqrt{x}(\sqrt{x}-1)}-\frac{2\sqrt{x}-1}{\sqrt{x}(\sqrt{x}-1)}\)
\(=\frac{x-2\sqrt{x}+1}{\sqrt{x}(\sqrt{x}(\sqrt{x}-1)}=\frac{(\sqrt{x}-1)^2}{\sqrt{x}(\sqrt{x}-1)}=\frac{\sqrt{x}-1}{\sqrt{x}}\)
b. \(A=3B\Leftrightarrow 2=\frac{3(\sqrt{x}-1)}{\sqrt{x}}\)
\(\Leftrightarrow 2\sqrt{x}=3(\sqrt{x}-1)\Leftrightarrow \sqrt{x}=3\Leftrightarrow x=9\)
