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\(A=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\) \(\left(\sqrt{6}+11\right)\)
\(A=\left(\frac{3.\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}{\sqrt{6}+1}\right)+\left(\frac{2.\left(\sqrt{6}+2\right)\left(\sqrt{6}-2\right)}{\sqrt{6}-2}\right)-\frac{4.\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{3-\sqrt{6}}\)\(\left(\sqrt{6}+11\right)\)
\(A=\left(3.\left(\sqrt{6}-1\right)+2.\left(\sqrt{6}+2\right)-4.\left(3+\sqrt{6}\right)\right)\left(\sqrt{6}+11\right)\)
\(A=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)=-115\)
Mình ghi nhầm. \(x=\frac{\sqrt{4+2\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)nhé
Bài 1:
a) \(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{2}-\frac{2\left(\sqrt{3}-1\right)}{2}\)
\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)=2\)
b) \(\frac{2}{5-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{\left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right)}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{\left(\sqrt{6}+\sqrt{3}\right)\left(\sqrt{6}-\sqrt{3}\right)}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{2}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{3}\)
\(=5+\sqrt{3}+\sqrt{6}-\sqrt{3}=5+\sqrt{6}\)
c) ĐK: \(a\ge0;a\ne1\)
\(\left(1+\frac{a+\sqrt{a}}{1+\sqrt{a}}\right).\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{1+\sqrt{a}}\right).\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)+a\)
\(=1-a+a=1\)
\(\sqrt{11-2\sqrt{30}}:\left(1-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(\sqrt{11-2\sqrt{3}\sqrt{5}\sqrt{2}}:\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}}\)
\(\sqrt{\left(\sqrt{3}\sqrt{2}\right)^2-2\sqrt{3}\sqrt{5}\sqrt{2}+\sqrt{5}^2}.\frac{\sqrt{6}}{\sqrt{6}-\sqrt{5}}\)
\(\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}.\frac{\sqrt{6}}{\sqrt{6}-\sqrt{5}}\)
\(\left(\sqrt{6}-\sqrt{5}\right).\frac{\sqrt{6}}{\sqrt{6}-\sqrt{5}}\)
\(=\sqrt{6}\)
\(\sqrt{11-2\sqrt{30}}:\left(1-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(=\sqrt{6-2\sqrt{30}+5}:\left(1-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(=\sqrt{\left(\sqrt{6}\right)^2-2\sqrt{30}+\left(\sqrt{5}\right)^2}:\left(1-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(=\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}:\left(1-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(=\left|\sqrt{6}-\sqrt{5}\right|:\left(\frac{\sqrt{6}}{\sqrt{6}}-\frac{\sqrt{5}}{\sqrt{6}}\right)\)
\(=\left(\sqrt{6}-\sqrt{5}\right):\left(\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}}\right)\)
\(=\left(\sqrt{6}-\sqrt{5}\right).\frac{\sqrt{6}}{\sqrt{6}-\sqrt{5}}\)
\(=\sqrt{6}\)