TN
1
K
Khách
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KT
26 tháng 7 2018
\(A=\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\)
\(=\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{\left(5-\sqrt{21}\right)\left(5+\sqrt{21}\right)}}+\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{\left(5-\sqrt{21}\right)\left(5+\sqrt{21}\right)}}\)
\(=\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{4}}+\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{4}}\)
\(=\frac{5+\sqrt{21}}{2}+\frac{5-\sqrt{21}}{2}=5\)
\(B=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)
\(\Rightarrow\)\(\sqrt{2}B=\sqrt{14+2\sqrt{33}}+\sqrt{14-2\sqrt{33}}\)
\(=\sqrt{\left(\sqrt{11}+\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}\)
\(=\sqrt{11}+\sqrt{3}+\sqrt{11}-\sqrt{3}=2\sqrt{11}\)
\(\Rightarrow\)\(B=\sqrt{22}\)
LH
1
CM
12 tháng 12 2017
\(\sqrt{21-8\sqrt{5}}\)\(-\sqrt{21-4\sqrt{5}}\)
\(=\sqrt{16-2.4\sqrt{5}+5}\)\(-\sqrt{20-2\sqrt{20}+1}\)
\(=\sqrt{\left(4-\sqrt{5}\right)^2}\)\(-\sqrt{\left(\sqrt{20}-1\right)}\)
\(=4-\sqrt{5}-\left(\sqrt{20}-1\right)\)
\(=4-\sqrt{5}-\sqrt{20}+1\)
\(=5-\sqrt{5}-2\sqrt{5}\)
\(=5-3\sqrt{5}\)
DN
0
28 tháng 6 2019
a. \(=\sqrt{2}.\left(\sqrt{7}+\sqrt{8}\right)\sqrt{5-\sqrt{3}\sqrt{7}}\)
\(=\left(\sqrt{7}+\sqrt{8}\right)\sqrt{3-2\sqrt{3}.\sqrt{7}+7}\)
\(=\left(\sqrt{7}+\sqrt{8}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\left(\sqrt{7}+\sqrt{8}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
Rồi nhân ra. bạn làm tiếp nhé. Tuy nhiên minh nghĩ bạn bị nhầm đề. là \(\sqrt{6}\) chứ không phải căn 16
b. \(=\frac{5\left(\sqrt{21}+1\right)}{21-16}+\frac{\sqrt{3}.\sqrt{7}\left(\sqrt{3}-\sqrt{7}\right)}{-\left(\sqrt{3}-\sqrt{7}\right)}\)
\(=\sqrt{21}+4-\sqrt{21}=4\)
8 tháng 7 2018
\(\sqrt{3+\sqrt{5}}=\frac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{5+2\sqrt{5}+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}+1}{\sqrt{2}}\)
\(\sqrt{7+3\sqrt{5}}=\frac{\sqrt{14+2.3\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{9+2.3\sqrt{5}+5}}{\sqrt{2}}=\frac{\sqrt{\left(3+\sqrt{5}\right)^2}}{\sqrt{2}}=\frac{3+\sqrt{5}}{\sqrt{2}}\)
\(\sqrt{21+6\sqrt{6}}=\sqrt{3+2.\sqrt{3}.3\sqrt{2}+18}=\sqrt{\left(\sqrt{3}+3\sqrt{2}\right)^2}=\sqrt{3}+3\sqrt{2}\)
\(\sqrt{21-6\sqrt{6}}=\sqrt{18-2.3\sqrt{2}.\sqrt{3}+3}=\sqrt{\left(3\sqrt{2}-\sqrt{3}\right)^2}=3\sqrt{2}-\sqrt{3}\)
Nên \(E=\frac{\sqrt{5}+1+3+\sqrt{5}}{\sqrt{2}}.\left(3\sqrt{2}+\sqrt{3}+3\sqrt{2}-\sqrt{3}\right)\)
\(=\frac{4+2\sqrt{5}}{\sqrt{2}}.2.3.\sqrt{2}=24+12\sqrt{5}\)
21 tháng 8 2018
\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)
\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16-2\cdot4\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)
\(=\sqrt{5}+1+4-\sqrt{5}\)( vì \(\sqrt{5}+1>0\)và \(4-\sqrt{5}>0\))
\(=5\)
IS
21 tháng 8 2018
\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)
\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16+8\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)
\(=\left|\sqrt{5}+1\right|+\left|4-\sqrt{5}\right|\)
\(=\sqrt{5}+1+4-\sqrt{5}\)
\(=5\)
LD
1
\(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}\)
\(=\sqrt{\frac{2\left(5+\sqrt{21}\right)}{2}}+\sqrt{\frac{2\left(5-\sqrt{21}\right)}{2}}\)
\(=\sqrt{\frac{10+2\sqrt{21}}{2}}+\sqrt{\frac{10-2\sqrt{21}}{2}}\)
\(=\sqrt{\frac{3+2\sqrt{21}+7}{2}}+\sqrt{\frac{3-2\sqrt{21+7}}{2}}\)
\(=\sqrt{\frac{\left(\sqrt{3}+\sqrt{7}\right)}{2}}+\sqrt{\frac{\left(\sqrt{3}+\sqrt{7}\right)}{2}}\)
\(=\frac{\left|\sqrt{3}+\sqrt{7}\right|}{2}+\frac{\left|\sqrt{3}-\sqrt{7}\right|}{2}\)
\(=\frac{\sqrt{3}+\sqrt{7}-\sqrt{3}-\sqrt{7}}{2}\)
\(=\sqrt{\frac{6}{2}}=\sqrt{3}\)