Question

Tính giá trị của M = \(\left(x^3+12x-9\right)^{2014}\) khi \(x=\sqrt[3]{4\left(\sqrt{5}+1\right)}-\sqrt[3]{4\left(\sqrt{5}-1\right)}\)

Answer 1

\(x=\sqrt[3]{4\left(\sqrt{5}+1\right)}-\sqrt[3]{4\left(\sqrt{5}-1\right)}\)

\(\Leftrightarrow x^3=4\left(\sqrt{5}+1\right)-4\left(\sqrt{5}-1\right)-3.\sqrt[3]{4\left(\sqrt{5}+1\right).4\left(\sqrt{5}-1\right)}x\)

\(\Leftrightarrow x^3=8-3.\sqrt[3]{4^2.\left(5-1\right)}x\)

\(\Leftrightarrow x^3=8-3.4x=8-12x\)

\(\Rightarrow M=\left(x^3+12x-9\right)^{2014}=\left(8-12x+12x-9\right)^{2014}=\left(-1\right)^{2014}=1\)