Question

giúp t vsssssss

tính giá trị biếu thức:

Answer 1

Đặt \(x=\sqrt[3]{9+4\sqrt[]{5}}+\sqrt[3]{9-4\sqrt[]{5}}\)

\(\Rightarrow x^3=18+3\sqrt[3]{\left(9+4\sqrt[]{5}\right)\left(9-4\sqrt[]{5}\right)}\left(\sqrt[3]{9+4\sqrt[]{5}}+\sqrt[3]{9-4\sqrt[]{5}}\right)\)

\(\Rightarrow x^3=18+3.1.x\)

\(\Rightarrow x^3-3x-18=0\)

\(\Rightarrow\left(x-3\right)\left(x^2+3x+6\right)=0\)

\(\Rightarrow x-3=0\)

\(\Rightarrow x=3\)

Vậy \(\sqrt[3]{9+4\sqrt[]{5}}+\sqrt[3]{9-4\sqrt[]{5}}=3\)