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a, = \(\frac{\sqrt{7}-5}{2}-\frac{2\left(3-\sqrt{7}\right)}{4}+\frac{6\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{5\left(4-\sqrt{7}\right)}{\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)}\)
\(\left(\sqrt{4,5}-\frac{1}{2}.\sqrt{72}+5\sqrt{\frac{1}{2}}\right).\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
=\(\left(\frac{3\sqrt{2}}{2}-3\sqrt{2}+\frac{5\sqrt{2}}{2}\right).\left(35\sqrt{6}-5\sqrt{6}-28\sqrt{6}\right)\)
=\(\left(\frac{3\sqrt{2}-6\sqrt{2}+5\sqrt{2}}{2}\right).2\sqrt{6}\)
=\(2\sqrt{2}.\sqrt{6}=4\sqrt{3}\)
\(\frac{4}{\sqrt{3}+1}-\frac{5}{\sqrt{3}-2}+\frac{6}{\sqrt{3}-3}=\frac{4\left(\sqrt{3}-1\right)}{2}+\frac{5\left(2+\sqrt{3}\right)}{4-3}+\frac{\sqrt{3}.2\sqrt{3}}{\sqrt{3}\left(1-\sqrt{3}\right)}\)
\(=2\sqrt{3}-2+10+5\sqrt{3}-\frac{2\sqrt{3}\left(\sqrt{3}+1\right)}{2}=7\sqrt{3}+8-3-\sqrt{3}=5+6\sqrt{3}\)
\(BT=\frac{2\sqrt{3}}{3+\sqrt{3}}-\frac{1}{\sqrt{3}-2}+\frac{6}{\sqrt{3}+3}=\frac{6+2\sqrt{3}}{3+\sqrt{3}}-\frac{1}{\sqrt{3}-2}=2-\frac{1}{\sqrt{3}-2}\)
\(=\frac{2\sqrt{3}-4-1}{\sqrt{3}-2}=\frac{2\sqrt{3}-5}{\sqrt{3}-2}=\left(5-2\sqrt{3}\right)\left(2+\sqrt{2}\right)=10+5\sqrt{2}-4\sqrt{3}+2\sqrt{6}\)
Nếu tính không lầm thì như vậy.
sao a ko trục căn thức từng phân thức cho nhanh ?
\(\frac{2}{\sqrt{3}+1}-\frac{1}{\sqrt{3}-2}+\frac{6}{\sqrt{3}+3}\)
\(=\frac{2\left(\sqrt{3}-1\right)}{2}-\frac{\sqrt{3}+2}{-1}+\frac{6\left(\sqrt{3}-3\right)}{-6}\)
\(=\sqrt{3}-1+\sqrt{3}+2-\sqrt{3}+3=\sqrt{3}+4\)