Question

[Song Minguk]

Cho  \(A=\sqrt{11+\sqrt{96}}\) và  \(B=\frac{2\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}\)

So sánh A và B

Answer 1

[Hoàng Lê Bảo Ngọc]

\(A=\sqrt{11+\sqrt{96}}=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}=2\sqrt{2}+\sqrt{3}\)

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

Xét : \(A-B=2\sqrt{2}+\sqrt{3}-\left(1+\sqrt{2}+\sqrt{3}\right)=\sqrt{2}-1>0\)

\(\Rightarrow A>B\)