Question

Tính

a)B=\(\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)

b)C=\(\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\)

Answer 1

\(B=\sqrt[3]{10+6\sqrt{3}}+\sqrt[3]{10-6\sqrt{3}}\)

\(\Rightarrow B^3=20+3B\sqrt[3]{10^2-36.3}\)

\(\Rightarrow B^3=20-6B\)

\(\Rightarrow B^3+6B-20=0\)

\(\Rightarrow\left(B-2\right)\left(B^2+2B+10\right)=0\)

\(\Rightarrow B=2\)

\(C^3=14+3C\sqrt[3]{49-25.2}\)

\(\Rightarrow C^3=14-3C\)

\(\Rightarrow C^3+3C-14=0\)

\(\Rightarrow\left(C-2\right)\left(C^2+2C+7\right)=0\)

\(\Rightarrow C=2\)