Question

tìm các số nguyên x thõa mãn : lx+3l +lx+4l+lx+5l=4x

Answer 1

Do \(\left|x+3\right|+\left|x+4\right|+\left|x+5\right|\ge0\Rightarrow4x\ge0\Rightarrow x\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}x+3>0\\x+4>0\\x+5>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left|x+3\right|=x+3\\\left|x+4\right|=x+4\\\left|x+5\right|=x+5\end{matrix}\right.\)

Phương trình trở thành:

\(x+3+x+4+x+5=4x\Leftrightarrow3x+12=4x\)

\(\Rightarrow x=12\) (t/m)