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\(\frac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}\)
= \(\frac{\sqrt{2^2-2\sqrt{5}2+\sqrt{5^2}}}{2-\sqrt{5}}\)
= \(\frac{\sqrt{\left(2-\sqrt{5}\right)^2}}{2-\sqrt{5}}\)
= \(\frac{\sqrt{5}-2}{2-\sqrt{5}}\)
= -1
Chúc bạn làm bài tốt :)
\(\frac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)Rút gọn
=\(\frac{\left(\sqrt{5}-2\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)-\left(2\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
=\(\frac{5-\sqrt{15}-2\sqrt{15}+6-10-2\sqrt{15}-\sqrt{15}-3}{5-3}\)
\(=\frac{-2-6\sqrt{15}}{2}=\frac{-2\left(1+3\sqrt{15}\right)}{3}=-1-3\sqrt{15}\)
B=\(\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}=\frac{6\left(1-\sqrt{3}\right)}{1-\sqrt{3}}+\frac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=6+3=9\)
C=\(\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}=\frac{3\left(1+\sqrt{3}\right)}{\sqrt{3}}+\frac{\sqrt{3}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}=\sqrt{3}+1-\sqrt{3}=1\)
D=\(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}=\frac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
E=\(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}=\frac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}+\frac{1}{2-\sqrt{3}}=\sqrt{3}+\frac{1}{2-\sqrt{3}}=\frac{2\sqrt{3}-1}{2-\sqrt{3}}\)
\(A=\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(=\frac{6+2\sqrt{5}}{2+\sqrt{6+2\sqrt{5}}}+\frac{6-2\sqrt{5}}{2-\sqrt{6-2\sqrt{5}}}\)
\(=\frac{6+2\sqrt{5}}{2+\sqrt{5+2\sqrt{5}+1}}+\frac{6-2\sqrt{5}}{2+\sqrt{5-2\sqrt{5}+1}}\)
\(=\frac{6+2\sqrt{5}}{2+\sqrt{\left(\sqrt{5}+1\right)^2}}+\frac{6-2\sqrt{5}}{2+\sqrt{\left(\sqrt{5}-1\right)^2}}\)
\(=\frac{6+2\sqrt{5}}{2+\left|\sqrt{5}+1\right|}+\frac{6-2\sqrt{5}}{2-\left|\sqrt{5}-1\right|}\)
\(=\frac{6+2\sqrt{5}}{2+\sqrt{5}+1}+\frac{6-2\sqrt{5}}{2-\sqrt{5}+1}\)( vì \(\sqrt{5}+1>0;\sqrt{5}-1>0\))
\(=\frac{6+2\sqrt{5}}{3+\sqrt{5}}+\frac{6-2\sqrt{5}}{3-\sqrt{5}}\)
\(=2+2\)
\(=4\)
Vậy A = 4
Tích cho mk nhoa !!!! ~~