Giải:
a) \(A=\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
\(\Leftrightarrow A=\sqrt{5-4\sqrt{5}+4}-\sqrt{5+4\sqrt{5}+4}\)
\(\Leftrightarrow A=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(\sqrt{5}+2\right)^2}\)
\(\Leftrightarrow A=\left|\sqrt{5}-2\right|-\left|\sqrt{5}+2\right|\)
\(\Leftrightarrow A=\sqrt{5}-2-\sqrt{5}-2\left(\sqrt{5}>\sqrt{4}=2\right)\)
\(\Leftrightarrow A=-4\)
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b) \(B=\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
\(\Leftrightarrow B=11^2-\left(4\sqrt{3}\right)^2\)
\(\Leftrightarrow B=121-48=73\)
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c) \(C=\sqrt{4-2\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
\(\Leftrightarrow C=\sqrt{3-2\sqrt{3}+1}+\sqrt{3+4\sqrt{3}+4}\)
\(\Leftrightarrow C=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+4\right)^2}\)
\(\Leftrightarrow C=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+4\right|\)
\(\Leftrightarrow C=\sqrt{3}-1+\sqrt{3}+4\)
\(\Leftrightarrow C=2\sqrt{3}+3\)
Vậy ...
