\(x^3+27-x^2=2x\)
\(\Leftrightarrow x^3-x^2-2x+27=0\) (1)
Đặt t = \(x-\dfrac{1}{3}\)
\(\Rightarrow x=t+\dfrac{1}{3}\)
Khi đó:
(1)\(\Leftrightarrow\)\(\left(t+\dfrac{1}{3}\right)^3-\left(t+\dfrac{1}{3}\right)^2-2\left(t+\dfrac{1}{3}\right)+27=0\)\(\Leftrightarrow t^3-\dfrac{7}{3}t+\dfrac{709}{23}=0\) (2)
Đặt \(y=\dfrac{t}{\dfrac{2\sqrt{7}}{3}}\) \(\Rightarrow t=\dfrac{2\sqrt{7}}{3}y\)
\(\Rightarrow\left(2\right)\Leftrightarrow4y^3-3y=-22,4701053\)
Đặt a = \(\sqrt[3]{-22,4701053+\sqrt{-22,4701053^2+1}}\)
\(\alpha=\dfrac{1}{2}\left(a-\dfrac{1}{a}\right)\) ; ta được:
\(4\alpha^3+3\alpha=-22,4701053\)
\(\Leftrightarrow y=\alpha\) là nghiệm của pt
\(\Rightarrow y=\dfrac{1}{2}\left(\sqrt[3]{-22,4701053+\sqrt{-22,4701053^2+1}}\right)\)\(\left(\sqrt[3]{-22.4701053-\sqrt{-22,4701053^2+1}}\right)\)\(=-1,63734063\)
\(\Rightarrow t=\dfrac{2\sqrt{7}}{3}.y=-2,887997412\)
\(\Rightarrow x=t+\dfrac{1}{3}=-2,554664079\)
