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a, \(\frac{1}{\left(\sqrt{3}+\sqrt{2}\right)^2}\) +\(\frac{1}{\left(\sqrt{3}-\sqrt{2}\right)^2}\) =\(\frac{\left(\sqrt{3}+\sqrt{2}\right)^2+\left(\sqrt{3}-\sqrt{2}\right)^2}{\left(\sqrt{3}+\sqrt{2}\right)^2\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\frac{10}{1}=10\)
mấy câu còn lại bạn tự làm nốt nhé mk ban rồi
a, = \(\frac{\sqrt{7}-5}{2}-\frac{2\left(3-\sqrt{7}\right)}{4}+\frac{6\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{5\left(4-\sqrt{7}\right)}{\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)}\)
a) \(\sqrt{17}-4\) b) \(\sqrt{3}\) c) \(\frac{\sqrt{2}}{2}\) d)\(\frac{\sqrt{x}+1}{\sqrt{x}-1}\) e) \(x-\sqrt{5}\)
f) \(4+2\sqrt{3}\) g) \(3+2\sqrt{2}\) h) \(x+\sqrt{x}+1\) i) \(\frac{3\sqrt{5}-\sqrt{15}}{10}\)
k) \(\sqrt{5}+\sqrt{6}\) i) 5 h) 0 l) \(\sqrt{5}+\sqrt{3}\) m) \(\frac{20\sqrt{3}}{3}\) d) 0
\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{1}{\sqrt{2}-1}+\frac{4}{3-\sqrt{5}}\)
\(=\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}+\frac{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}{\sqrt{2}-1}\)
\(-\frac{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}{3-\sqrt{5}}\)
\(=\sqrt{5}+\sqrt{2}+\sqrt{2}+1-3-\sqrt{5}\)
\(=2\sqrt{2}-2\)
\(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{4}{3+\sqrt{3}}\)
\(=\frac{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}{2+\sqrt{3}}+\frac{1}{\sqrt{3}}-\frac{4}{3+\sqrt{3}}\)
\(=2-\sqrt{3}+\frac{1}{\sqrt{3}}-\frac{4}{3+\sqrt{3}}\)