Question

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

Các bạn giúp mình với nha :)) cảm ơn các bạn nhiều ạ <3

Answer 1

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

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

\(=5\cdot\dfrac{1}{2}\cdot3+\dfrac{1}{2}\cdot\left(5\right)=\dfrac{15}{2}+\dfrac{5}{2}=10\)