Question

Tìm x biết

2014.Ix-12I+(x-12)²=2013.I12-xI

Answer 1

\(2014\left|x-12\right|+\left(x-12\right)^2=2013\left|12-x\right|\)

\(\Leftrightarrow2014\left|x-12\right|+\left(x-12\right)^2=2013\left|x-12\right|\)

Đặt \(t=\left|x-12\right|\left(t\ge0\right)\) ta có:

\(2014t+t^2=2013t\)

\(\Leftrightarrow t^2+t=0\)\(\Leftrightarrow t\left(t+1\right)=0\)\(\Leftrightarrow\left[\begin{array}{nghiempt}t=0\\t=-1\left(loai\right)\end{array}\right.\)

Với \(t=0\Rightarrow\left|x-12\right|=0\Rightarrow x-12=0\Rightarrow x=12\)

Vậy x=12