Question

Biết \(A=\sqrt[3]{200+8\sqrt{5}}=a+b\sqrt{5}\)

Khi đó giá trị a-b là :

Answer 1

\(A=\sqrt[3]{200+80\sqrt{5}}\) (sửa)

\(A=\sqrt[3]{125+75\sqrt{5}+75+5\sqrt{5}}\)

\(A=\sqrt[3]{5^3+3\cdot5^2\cdot\sqrt{5}+3\cdot5\cdot\left(\sqrt{5}\right)^2+\left(\sqrt{5}\right)^3}\)

\(A=\sqrt[3]{\left(5+\sqrt{5}\right)^3}\)

\(A=5+\sqrt{5}\)

\(\Rightarrow a=5;b=1\)

\(\Rightarrow a-b=5-1=4\)