Question

\(2x^{3}-x^{2}+\sqrt[3]{2x^{3}-3x+1}=3x+1+\sqrt[3]{x^{2}+2}\)

GIúp mình giải bài toán này với..

Answer 1

\(Pt\Leftrightarrow2x^3-x^2-3x-1+\sqrt[3]{2x^3-3x+1}-\sqrt[3]{x^2+2}=0\\ \Leftrightarrow2x^3-x^2-3x-1+\dfrac{2x^3-3x+1-x^2-2}{A^2+B^2+AB}=0\left(A=\sqrt[3]{2x^3-3x+1},B=\sqrt[3]{x^2+2}\right)\\ \Leftrightarrow2x^3-x^2-3x-1=0\left(A^2+B^2+AB>0\right)\\ \Leftrightarrow\left(2x+1\right)\left(x^2-x-1\right)=0\\ \left[{}\begin{matrix}x=-\dfrac{1}{2}\\\dfrac{1+\sqrt{5}}{2}\\\dfrac{1-\sqrt{5}}{2}\end{matrix}\right.\Leftrightarrow\)