Question

a) \(\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)

b) \(\dfrac{1}{\sqrt[3]{4-\sqrt{15}}}+\sqrt[3]{4-\sqrt{15}}\)

c) \(\dfrac{\sqrt[3]{a^4}+\sqrt[3]{a^2b^2}+\sqrt[3]{b^4}}{\sqrt[3]{a^2}+\sqrt[3]{ab}+\sqrt[3]{b^2}}\)

Rút gọn các biểu thức sau

Answer 1

b: \(A=\dfrac{1}{\sqrt[3]{4-\sqrt{15}}}+\sqrt[3]{4-\sqrt{15}}\)

\(=\sqrt[3]{4+\sqrt{15}}+\sqrt[3]{4-\sqrt{15}}\)

\(\Leftrightarrow A^3=4+\sqrt{15}+4-\sqrt{15}+3\cdot A\cdot1\)

\(\Leftrightarrow A^3-3A-8=0\)

hay \(A\simeq2.49\)

a: \(B=\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)

\(\Leftrightarrow B^3=5-\sqrt{17}+5+\sqrt{17}+3\cdot B\cdot2=10+6B\)

\(\Leftrightarrow B^3-6B-10=0\)

hay \(B\simeq3.05\)