Question

Tìm x biết :

\(\left(x-3\right)^2-x\left|x-3\right|=0\)

Answer 1

\(\left(x-3\right)^2-x\left|x-3\right|=0\)

\(\Rightarrow\left|x-3\right|^2-x\left|x-3\right|=0\)

Đặt: \(\left|x-3\right|=t\) ta có: \(pt\Leftrightarrow t^2-xt=0\)

\(\Rightarrow t\left(x-t\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}t=0\\x=t\end{matrix}\right.\)

Với \(t=0\) ta được \(x=3\)

Với \(x=t\) ta có: \(x=\left|x-3\right|\)

\(\Rightarrow\left[{}\begin{matrix}x=x-3\left(x\ge3\right)\\x=3-x\left(x< 3\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3=0\left(vl\right)\\x=\dfrac{3}{2}\left(tm\right)\end{matrix}\right.\)

Vậy pt có nghiệm: \(S=\left\{0;\dfrac{3}{2}\right\}\)