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a: \(=\sqrt{5}+2+\sqrt{3}+1-\sqrt{5}-\sqrt{3}=3\)
b: \(=\left(-\sqrt{5}-2+\sqrt{5}-\sqrt{3}\right)\cdot\left(2\sqrt{3}+3\right)\)
\(=-\sqrt{3}\left(2+\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)\)
\(=-\sqrt{3}\left(7+4\sqrt{3}\right)=-7\sqrt{3}-12\)
c: \(=\dfrac{\sqrt{2}+\sqrt{3}+2}{\left(\sqrt{2}+\sqrt{3}+2\right)+\sqrt{2}\left(\sqrt{2}+\sqrt{3}+2\right)}=\dfrac{1}{1+\sqrt{2}}=\sqrt{2}-1\)
1.
\(\Leftrightarrow x-3=\dfrac{1}{8}\)
\(\Leftrightarrow x=\dfrac{25}{8}\)
b: \(=\dfrac{\sqrt{5}+1}{\sqrt{5}-1}+\dfrac{\sqrt{5}-1}{\sqrt{5}+1}\)
\(=\dfrac{6+2\sqrt{5}+6-2\sqrt{5}}{4}=\dfrac{12}{4}=3\)
c: \(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)
e: \(=\dfrac{2\sqrt{3+\sqrt{5-2\sqrt{3}-1}}}{\sqrt{6}-\sqrt{2}}\)
\(=\dfrac{\sqrt{2}\cdot\sqrt{3+\sqrt{3}-1}}{\sqrt{3}-1}=\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{3}-1}=\dfrac{\sqrt{3}+1}{\sqrt{3}-1}\)
\(=\dfrac{4-2\sqrt{3}}{2}=2-\sqrt{3}\)
\(a.\sqrt{\dfrac{\left(1-\sqrt{3}\right)^2}{9}}+\dfrac{2}{4+\sqrt{4-2\sqrt{3}}}=\dfrac{\sqrt{3}-1}{3}+\dfrac{2}{4+\sqrt{3-2\sqrt{3}+1}}=\dfrac{\sqrt{3}-1}{3}+\dfrac{2}{3+\sqrt{3}}=\dfrac{3-1+2\sqrt{3}}{3\left(\sqrt{3}+1\right)}=\dfrac{2\left(\sqrt{3}+1\right)}{3\left(\sqrt{3}+1\right)}=\dfrac{2}{3}\)
\(b.\dfrac{\sqrt{\sqrt{5}+\sqrt{2}}}{\sqrt{3\sqrt{5}-3\sqrt{2}}}=\sqrt{\dfrac{\sqrt{5}+\sqrt{2}}{3\left(\sqrt{5}-\sqrt{2}\right)}}=\sqrt{\dfrac{\left(\sqrt{5}+\sqrt{2}\right)^2}{3.3}}=\dfrac{\sqrt{5}+\sqrt{2}}{3}\)