Question

[Châu Đặng Huỳnh Bảo]

Rút gọn B=\(5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\frac{5}{2}}\right)^2+\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\frac{5}{2}}\right)^2\)

Answer 1

[Mêlinh]

em mới học lớp 5

Answer 2

[Hoàng Lê Bảo Ngọc]

\(2B=5\left(\sqrt{4+2\sqrt{3}}+\sqrt{6-2\sqrt{5}}-\sqrt{5}\right)^2+\left(\sqrt{4-2\sqrt{3}}+\sqrt{6+2\sqrt{5}}-\sqrt{5}\right)^2 \)

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

\(=5\left(\sqrt{3}\right)^2+\left(\sqrt{3}\right)^2=5.3+3=18\)

\(\Rightarrow B=9\)