Rut gon:
\(\frac{1}{2\sqrt{2}}-\frac{3}{2}\sqrt{\frac{9}{2}}+\frac{2}{5}\sqrt{30}\)
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8 tháng 8 2016
1) \(\frac{\sqrt{6-2\sqrt{5}}}{2-2\sqrt{5}}=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}}{2\left(1-\sqrt{5}\right)}=\frac{\sqrt{5}-1}{2\left(1-\sqrt{5}\right)}=-\frac{1}{2}\)
2) \(\frac{\sqrt{7-4\sqrt{3}}}{1-\sqrt{3}}=\frac{\sqrt{\left(2-\sqrt{3}\right)^2}}{1-\sqrt{3}}=\frac{2-\sqrt{3}}{1-\sqrt{3}}\)
2 tháng 10 2017
ĐKXĐ:\(x\ge0,x\ne4\)\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)-2-5\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}+2\right)}\)=\(\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)=\(\frac{3\sqrt{x}}{\sqrt{x}+2}\)
\(\frac{1}{2\sqrt{2}}-\frac{3}{2}\sqrt{\frac{9}{2}}+\frac{2}{5}\sqrt{30}=\frac{1}{2\sqrt{2}}-\frac{3}{2}.\frac{\sqrt{9}}{\sqrt{2}}+\frac{2\sqrt{30}}{5}\)
\(=\frac{1}{2\sqrt{2}}-\frac{9}{2\sqrt{2}}+\frac{2\sqrt{30}}{5}=\frac{-8}{2\sqrt{2}}+\frac{2\sqrt{30}}{5}\)
\(=\frac{-4}{\sqrt{2}}+\frac{2\sqrt{30}}{5}=\frac{-4\sqrt{2}}{2}+\frac{2\sqrt{30}}{5}\)
\(=\frac{-20\sqrt{2}}{10}+\frac{4\sqrt{30}}{10}=\frac{-20\sqrt{2}+4\sqrt{30}}{10}=\frac{2.\left(2\sqrt{30}-10\sqrt{2}\right)}{10}\)
\(=\frac{2\sqrt{30}-10\sqrt{2}}{5}\)
\(\frac{1}{2\sqrt{2}}-\frac{3}{2}\sqrt{\frac{9}{2}}+\frac{2}{5}\sqrt{30}=\frac{1}{2\sqrt{2}}-\frac{3}{2}.\frac{\sqrt{9}}{\sqrt{2}}+\frac{2\sqrt{30}}{5}=\frac{\sqrt{2}}{4}-\frac{9\sqrt{2}}{4}+\frac{2\sqrt{30}}{5}=-2\sqrt{2}+\frac{2\sqrt{30}}{5}=\frac{2\sqrt{30}-10\sqrt{2}}{5}\)