Trả lời:
Đặt \(B=\sqrt[3]{\frac{1}{4}+\frac{\sqrt{5}}{8}}-\sqrt[3]{\frac{\sqrt{5}}{8}-\frac{1}{4}}\)
\(4B=4.\sqrt[3]{\frac{1}{4}+\frac{\sqrt{5}}{8}}-4.\sqrt[3]{\frac{\sqrt{5}}{8}-\frac{1}{4}}\)
\(4B=\sqrt[3]{64.\left(\frac{1}{4}+\frac{\sqrt{5}}{8}\right)}-\sqrt[3]{64.\left(\frac{\sqrt{5}}{8}-\frac{1}{4}\right)}\)
\(4B=\sqrt[3]{16+8\sqrt{5}}-\sqrt[3]{5\sqrt{8}-16}\)
\(4B=\sqrt[3]{1+3\sqrt{5}+15+5\sqrt{5}}-\sqrt[3]{-\left(16-5\sqrt{8}\right)}\)
\(4B=\sqrt[3]{\left(1+\sqrt{5}\right)^3}-\sqrt[3]{-\left(1-3\sqrt{5}+15-5\sqrt{5}\right)}\)
\(4B=1+\sqrt{5}-\sqrt[3]{-\left(1-\sqrt{5}\right)^3}\)
\(4B=1+\sqrt{5}-\left[-\left(1-\sqrt{5}\right)\right]\)
\(4B=1+\sqrt{5}+1-\sqrt{5}\)
\(4B=2\)
\(B=\frac{1}{2}\)
