Question

\(\frac{x^4+4}{x^2-2}-5x=0\)

Answer 1

Lời giải:
ĐKXĐ: \(x\neq \pm \sqrt{2}\)

PT \(\Rightarrow x^4+4-5x(x^2-2)=0\)

\(\Leftrightarrow x^4-5x^3+10x+4=0\)

\(\Leftrightarrow x^3(x+1)-6x^2(x+1)+6x(x+1)+4(x+1)=0\)

\(\Leftrightarrow (x+1)(x^3-6x^2+6x+4)=0\)

\(\Leftrightarrow (x+1)[x^2(x-2)-4x(x-2)-2(x-2)]=0\)

\(\Leftrightarrow (x+1)(x-2)(x^2-4x-2)=0\)

\(\Rightarrow \left[\begin{matrix} x+1=0\\ x-2=0\\ x^2-4x-2=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=-1\\ x=2\\ x=2\pm \sqrt{6}\end{matrix}\right.\) (đều thỏa mãn)

Vậy...........