Question

Answer 1

a: \(A=\sqrt{20}-\sqrt{45}+\sqrt{6+2\sqrt{5}}\)

\(=2\sqrt{5}-3\sqrt{5}+\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=-\sqrt{5}+\sqrt{5}+1=1\)

b: \(B=\dfrac{a-a\sqrt{a}}{1-\sqrt{a}}+\dfrac{a+\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\)

\(=\dfrac{a\left(1-\sqrt{a}\right)}{1-\sqrt{a}}+\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}-\sqrt{a}\)

\(=a+\sqrt{a}-\sqrt{a}=a\)