Question

Rút gọn

a)\(A=\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

b)\(B=\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{5}}\)

Answer 1

a, \(A=\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

\(\dfrac{A}{\sqrt{2}}=\dfrac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\dfrac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)

\(\dfrac{A}{\sqrt{2}}=\dfrac{2+\sqrt{3}}{3+\sqrt{3}}+\dfrac{2-\sqrt{3}}{3-\sqrt{3}}\)

\(\dfrac{A}{\sqrt{2}}=\dfrac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{6}=1\)

\(\Rightarrow A=\sqrt{2}\)

Answer 2

nếu k có ai làm chiều tớ làm cho h lười quá

Answer 3

\(B=\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{5}}\)

\(=\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}-\sqrt{23-4\sqrt{5}}\)

\(=\sqrt{5}-\sqrt{3}-\sqrt{23-4\sqrt{5}}\)