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Ta có : \(\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}\)
\(=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2}=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{2\sqrt{6}}\)
\(=\frac{3\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{2\sqrt{2}}=\frac{3\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{4}\)
\(a,\frac{\sqrt{5}}{\sqrt{3-\sqrt{5}}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{\left(3-\sqrt{5}\right).\left(3+\sqrt{5}\right)}}\)
\(=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{9-5}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{4}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{2}\)
\(\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}\)
\(=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2+2\sqrt{2\cdot3}+3-5}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{5+2\sqrt{6}-5}=\frac{\sqrt{6}\cdot\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{\sqrt{6}\cdot2\sqrt{6}}=\frac{2\sqrt{3}+3\sqrt{2}-\sqrt{30}}{12}\)
Ta có \(\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\) = \(\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{5+2\sqrt{6}-5}\)
= \(\frac{\sqrt{6}\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{12}\)
\(\frac{2}{\sqrt{3}-5}=\frac{2\left(\sqrt{3}+5\right)}{3-5^2}=\frac{2\left(\sqrt{3}+5\right)}{-22}=\frac{-5-\sqrt{3}}{11}\)
\(A=\frac{1}{\sqrt{5}-\sqrt{3}+2}\)
\(A=\frac{1}{\left(\sqrt{5}+2\right)+\sqrt{3}}\)
\(A=\frac{1\left(\left(\sqrt{5}+2\right)-\sqrt{3}\right)}{\left(\left(\sqrt{5}+2\right)+3\right)\left(\left(\sqrt{5}+2\right)-\sqrt{3}\right)}\)
\(A=\frac{\sqrt{5}+2-\sqrt{3}}{\left(\sqrt{5}+2\right)^2-3}\)
\(A=\frac{\sqrt{5}+2-\sqrt{3}}{6-4\sqrt{5}}\)
\(A=\frac{\left(\sqrt{5}+2-\sqrt{3}\right)\left(6+4\sqrt{5}\right)}{\left(6-4\sqrt{5}\right)\left(6+4\sqrt{5}\right)}\)
\(A=\frac{6\sqrt{5}+20+12+8\sqrt{5}-6\sqrt{3}-4\sqrt{15}}{36-16\cdot5}\)
\(A=\frac{14\sqrt{5}+32-6\sqrt{3}-4\sqrt{15}}{-44}\)
\(A=\frac{6\sqrt{3}+4\sqrt{15}-14\sqrt{5}-32}{44}\)
Nhớ k cho mik đó nha ....... rồi kb lun ahihi
có công thức rồi mà cậu,bài này dễ,cậu thử áp dụng công thức xemm..
a) \(\frac{3}{\sqrt{5}}=\frac{3\sqrt{5}}{\sqrt{5}.\sqrt{5}}=\frac{3\sqrt{5}}{5}\)
\(\frac{2\sqrt{3}}{\sqrt{2}}=\frac{2\sqrt{3}.\sqrt{2}}{\sqrt{2}.\sqrt{2}}=\frac{2\sqrt{6}}{2}=\sqrt{6}\)
\(\frac{a}{\sqrt{b}}=\frac{a\sqrt{b}}{\sqrt{b}.\sqrt{b}}=\frac{a\sqrt{b}}{b}\)
\(\frac{x+1}{\sqrt{x^2-1}}=\frac{\left(x+1\right)\left(\sqrt{x^2-1}\right)}{\left(\sqrt{x^2-1}\right)\left(\sqrt{x^2-1}\right)}\) = \(\frac{\left(\sqrt{x^2-1}\right)\left(x+1\right)}{x^2-1}\)
bạn làm tương tự nha