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\((3\sqrt{20}-2\sqrt{80}+\frac{2}{3}\sqrt{45}-\sqrt{5}):\sqrt{5}\)
\(=\left(3\sqrt{2^2.5}-2\sqrt{4^2.5}+\frac{2}{3}\sqrt{3^2.5}-\sqrt{5}\right):\sqrt{5}\)
\(=\left(3.2\sqrt{5}-2.4\sqrt{5}+\frac{2}{3}.3\sqrt{5}\right):\sqrt{5}\)
\(=\left(6\sqrt{5}-8\sqrt{5}+2\sqrt{5}-\sqrt{5}\right):\sqrt{5}\)
\(=-\sqrt{5}:\sqrt{5}=-1\)
\(\left(\frac{2+\sqrt{5}}{2-\sqrt{5}}-\frac{2-\sqrt{5}}{2+\sqrt{5}}\right).\frac{5-\sqrt{5}}{1-\sqrt{5}}\)
\(=\left(\frac{\left(2+\sqrt{5}\right)^2}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}-\frac{\left(2-\sqrt{5}\right)^2}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}\right).\frac{\sqrt{5}\left(\sqrt{5}-1\right)}{1-\sqrt{5}}\)
\(=\left(\frac{4+4\sqrt{5}+5-\left(4-4\sqrt{5}+5\right)}{4-5}\right).\frac{-\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}\)
\(=\frac{9+4\sqrt{5}-9+4\sqrt{5}}{-1}.\left(-\sqrt{5}\right)\)
\(-8\sqrt{5}.\left(-\sqrt{5}\right)=40\)
\(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}-\dfrac{5-\sqrt{5}}{5+\sqrt{5}}=\dfrac{\left(5+\sqrt{5}\right)^2}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}-\dfrac{\left(5-\sqrt{5}\right)^2}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}=\dfrac{\left(5+\sqrt{5}\right)^2-\left(5-\sqrt{5}\right)^2}{25-5}=\dfrac{\left(5+\sqrt{5}-5+\sqrt{5}\right)\left(5+\sqrt{5}+5-\sqrt{5}\right)}{20}=\dfrac{\sqrt{5^2}.10}{20}=\dfrac{50}{20}=\dfrac{5}{2}\)
Lời giải:
\(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}=\frac{(5+\sqrt{5})^2+(5-\sqrt{5})^2}{(5-\sqrt{5})(5+\sqrt{5})}\)
\(=\frac{30+10\sqrt{5}+30-10\sqrt{5}}{25-5}=\frac{60}{20}=3\)
\(=\left(\sqrt{5}-1-5\right)\cdot\left(\frac{\sqrt{5}\left(1+\sqrt{5}\right)}{1+\sqrt{5}}+6\right)=\left(\sqrt{5}-6\right)\left(\sqrt{5}+6\right)=5-36=-31\)
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ok bn