Question

1.Tính: B=\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{7-2\sqrt{10}}\), giúp với mik đang cần gấp

Answer 1

\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{7-2\sqrt{10}}\)

\(=\dfrac{1}{\sqrt{6-2.\sqrt{6}.\sqrt{5}+5}}-\dfrac{3\left(7+2\sqrt{10}\right)}{\left(7-2\sqrt{10}\right)\left(7+2\sqrt{10}\right)}\)

\(=\dfrac{1}{\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}}-\dfrac{21+6\sqrt{10}}{49-40}\)

\(=\dfrac{1}{\sqrt{6}-\sqrt{5}}-\dfrac{21+6\sqrt{10}}{9}\)

\(=\dfrac{\left(\sqrt{6}+\sqrt{5}\right).9-21-6\sqrt{10}}{9}\)

\(=\dfrac{9\sqrt{6}+9\sqrt{5}-21-6\sqrt{10}}{9}=\dfrac{3\sqrt{6}+3\sqrt{5}-7-2\sqrt{10}}{3}\)