a) \(A=\dfrac{1}{3-\sqrt{10}}-\dfrac{1}{3+\sqrt{10}}\) \(=\dfrac{3+\sqrt{10}-3+\sqrt{10}}{\left(3-\sqrt{10}\right)\left(3+\sqrt{10}\right)}\) \(=\dfrac{2\sqrt{10}}{9-10}\) \(=\dfrac{2\sqrt{10}}{-1}=-2\sqrt{10}\)
b) \(B=\sqrt{11-6\sqrt{2}}-\sqrt{11+6\sqrt{2}}\) \(=\sqrt{9-6\sqrt{2}+2}-\sqrt{9+6\sqrt{2}+2}\) \(=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(3+\sqrt{2}\right)^2}\) \(=\left|3-\sqrt{2}\right|-\left|3+\sqrt{2}\right|\) \(=3-\sqrt{2}-3-\sqrt{2}\) \(=-2\sqrt{2}\)
c) \(C=\sqrt{8}-\sqrt{50}+\dfrac{3}{\sqrt{2}}\) \(=2\sqrt{2}-5\sqrt{2}+\dfrac{3\sqrt{2}}{2}\) \(=-3\sqrt{2}+\dfrac{3\sqrt{2}}{2}\) \(=\dfrac{-6\sqrt{2}+3\sqrt{2}}{2}\) \(=\dfrac{-3\sqrt{2}}{2}\)
a, A=\(\dfrac{1}{3-\sqrt{10}}-\dfrac{1}{3+\sqrt{10}}\)
A=\(\dfrac{3+\sqrt{10}}{\left(3-\sqrt{10}\right)\left(3+\sqrt{10}\right)}-\dfrac{3-\sqrt{10}}{\left(3+\sqrt{10}\right)\left(3-\sqrt{10}\right)}\)
A=\(\dfrac{3+\sqrt{10}}{-1}-\dfrac{3-\sqrt{10}}{-1}\)
A=\(-3-\sqrt{10}-\left(-3+\sqrt{10}\right)\)
A=\(-3-\sqrt{10}+3-\sqrt{10}\)
A=\(-2\sqrt{10}\)
b, B=\(\sqrt{11-6\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
B=\(\sqrt{9-6\sqrt{2}+2}-\sqrt{9+6\sqrt{2}+2}\)
B=\(\sqrt{3^2-6\sqrt{2}+\left(\sqrt{2}\right)^2}-\sqrt{3^2+6\sqrt{2}+\left(\sqrt{2}\right)^2}\)
B=\(\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(3+\sqrt{2}\right)^2}\)
B=\(\left|3-\sqrt{2}\right|-\left|3+\sqrt{2}\right|\)
B=\(3-\sqrt{2}-\left(3+\sqrt{2}\right)\)
B=\(3-\sqrt{2}-3-\sqrt{2}\)
B=\(-2\sqrt{2}\)
c,C= \(\sqrt{8}-\sqrt{50}+\dfrac{3}{\sqrt{2}}\)
C=\(\sqrt{4.2}-\sqrt{25.2}+\dfrac{3}{\sqrt{2}}\)
C=\(2\sqrt{2}-5\sqrt{2}+\dfrac{3}{\sqrt{2}}\)
C=\(-3\sqrt{2}+\dfrac{3}{\sqrt{2}}\)
C=\(\dfrac{-6}{\sqrt{2}}+\dfrac{3}{\sqrt{2}}\)
C=\(\dfrac{-3}{\sqrt{2}}=\dfrac{-3\sqrt{2}}{2}\)
