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Làm tới dòng thứ 3 máy đơ, 2 lần rồi T,T
Mình chia làm 2 phần tính nhé
\(A=\frac{4\sqrt{2}}{\sqrt{10-2\sqrt{21}}}+\frac{3}{\sqrt{15+6\sqrt{6}}}-\frac{1}{\sqrt{19-6\sqrt{10}}}\)
\(A=\frac{4\sqrt{2}}{\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}}+\frac{3}{\sqrt{\left(\sqrt{9}+\sqrt{6}\right)^2}}-\frac{1}{\sqrt{\left(\sqrt{10}-\sqrt{9}\right)^2}}\)
\(A=\frac{4\sqrt{2}}{\sqrt{7}-\sqrt{3}}+\frac{3}{3+\sqrt{6}}-\frac{1}{\sqrt{10}-3}\)
\(A=\frac{4\sqrt{2}\left(\sqrt{7}+\sqrt{3}\right)}{7-3}+\frac{3\left(3-\sqrt{6}\right)}{9-6}-\frac{1\left(\sqrt{10}+3\right)}{10-9}\)
\(A=\frac{4\sqrt{14}+4\sqrt{6}}{4}+\frac{9-3\sqrt{6}}{3}-\sqrt{10}-3\)
\(A=\sqrt{14}+\sqrt{6}+3-\sqrt{6}-\sqrt{10}-3\)
\(A=\sqrt{14}-\sqrt{10}\)
\(B=\sqrt{6+\sqrt{35}}\)
\(B=\frac{\sqrt{2}\left(\sqrt{6+\sqrt{35}}\right)}{\sqrt{2}}\)
\(B=\frac{\sqrt{12+2\sqrt{35}}}{\sqrt{2}}\)
\(B=\frac{\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}}{\sqrt{2}}\)
\(B=\frac{\sqrt{7}+\sqrt{5}}{\sqrt{2}}\)
\(\Rightarrow M=A.B=\left(\sqrt{14}-\sqrt{10}\right).\frac{\sqrt{7}+\sqrt{5}}{\sqrt{2}}\)
\(M=\sqrt{2}\left(\sqrt{7}-\sqrt{5}\right).\frac{\sqrt{7}+\sqrt{5}}{\sqrt{2}}\)
\(M=\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
\(M=\left(\sqrt{7}\right)^2-\left(\sqrt{5}\right)^2\)
\(M=7-5=2\)
- \(\frac{2+\sqrt{2}}{1+\sqrt{2}}=\frac{\sqrt{2}\left(1+\sqrt{2}\right)}{1+\sqrt{2}}=\sqrt{2}\)
- \(\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}=\frac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}=-\sqrt{5}\)
- \(\frac{2\sqrt{3}-\sqrt{6}}{1-\sqrt{3}}=\frac{-\sqrt{6}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}=-\sqrt{6}\)
- \(\frac{a-\sqrt{a}}{1-\sqrt{a}}=\frac{-\sqrt{a}\left(1-\sqrt{a}\right)}{1-\sqrt{a}}=-\sqrt{a}\)
- \(\frac{p-2\sqrt{p}}{\sqrt{p}-2}=\frac{\sqrt{p}\left(\sqrt{p}-2\right)}{\sqrt{p}-2}=\sqrt{p}\)
a) \(\frac{\sqrt{2.5}-\sqrt{2}}{\sqrt{5}-1}+\frac{\left(\sqrt{2}\right)^2-\sqrt{2}}{\sqrt{2}-1}\)
\(=\frac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\)
\(=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
b) \(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\)
\(=\frac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\)
\(=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
(Hai bài náy đều tương tự nhau bạn ạ, nhớ k cho mình với nhé, chúc bạn học tốt!)