Question

Tính giá trị của biểu thức sau :

a) \(A=\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}-\frac{9}{\sqrt{10}+1}\)

b) \(\frac{\left(2-\sqrt{3}\right)\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}+\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)2-\frac{3-\sqrt{3}}{\sqrt{3}-1}\)

Answer 1

a) \(A=\frac{\sqrt{5}\sqrt{2}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}-\frac{9\left(\sqrt{10}-1\right)}{9}=\sqrt{10}-\sqrt{10}-1=1\)

b) \(B=\frac{\left(2-\sqrt{3}\right)\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}+\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2-\frac{3-\sqrt{3}}{\sqrt{3}-1}\right)\)

\(=\sqrt{2-\sqrt{3}}.\sqrt{2+\sqrt{3}}+\left(2+\frac{\sqrt{3}\left(\sqrt{3+1}\right)}{\sqrt{3}+1}\right)\left(2-\frac{\sqrt{3}\left(\sqrt{3-1}\right)}{\sqrt{3}-1}\right)\)

= \(\sqrt{4-3}+\left(2+\sqrt{3}\right)\left(2+\sqrt{3}\right)=1+4-3=2\)

Answer 2

Sửa đề câu b

\(B=\frac{\left(2-\sqrt{3}\right)\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}+\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2-\frac{3-\sqrt{3}}{\sqrt{3}-1}\right)\)