1.
\(\dfrac{4}{\sqrt{5}-1}-\sqrt{\left(2-\sqrt{5}\right)^2}=\dfrac{4\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}-\left|2-\sqrt{5}\right|\)
\(=\dfrac{4\left(\sqrt{5}+1\right)}{4}-\left(\sqrt{5}-2\right)=\sqrt{5}+1-\sqrt{5}+2=3\)
2.
ĐKXĐ: \(x\ge0\)
\(\sqrt{2^2x}+\dfrac{1}{2}\sqrt{6^2x}=\sqrt{3^2.x}+2\)
\(\Leftrightarrow2\sqrt{x}+3\sqrt{x}=3\sqrt{x}+2\)
\(\Leftrightarrow2\sqrt{x}=2\)
\(\Leftrightarrow\sqrt{x}=1\)
\(\Leftrightarrow x=1\)
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