Question

Giải : \(\frac{x^3+x^2-x}{x\left|x-2\right|}=1\)

Answer 1

\(\frac{x^3+x^2-x}{x\left|x-2\right|}=1\left(ĐK:x\ne0;x\ne2\right)\)

\(\Leftrightarrow\frac{x^2+x-1}{\left|x-2\right|}=1\)

\(\Leftrightarrow x^2+x-1=\left|x-2\right|\) (*)

Với: \(x\ge2\) (*) trở thành:

\(x^2+x-1=x-2\Leftrightarrow x^2+1=0\left(loai\right)\)

Với: \(x< 2\) thì (*) trở thành:

\(x^2+x-1=2-x\Leftrightarrow x^2+2x-3=0\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[\begin{matrix}x=1\left(tm\right)\\x=-3\left(tm\right)\end{matrix}\right.\)