\(\left|x+123\right|+\left|\left|y+1\right|-5\right|=0\)
Ta có: \(\left|x+123\right|\ge0\) với mọi x
\(\left|\left|y+1\right|-5\right|\ge0\) với mọi y
Nên \(\left|x+123\right|+\left|\left|y+1\right|-5\right|=0\)
\(\Rightarrow\left\{{}\begin{matrix}x+123=0\\\left|y+1\right|-5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-123\\\left|y+1\right|=5\end{matrix}\right.\)
\(\left|y+1\right|=5\Rightarrow y+1=\pm5\)
+ \(y+1=-5\Rightarrow y=-6\)
+ \(y+1=5\Rightarrow y=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=-123\\\left[{}\begin{matrix}y=-6\\y=4\end{matrix}\right.\end{matrix}\right.\)
~ Học tốt ~
\(\left|x+123\right|+\left|\left|x+1\right|-5\right|=0\)
\(\left|x+123\right|\ge0;\left|\left|x+1\right|-5\right|\ge0\)
Dấu "=" xảy ra khi:
\(\left|x+123\right|=0\Rightarrow x+123=0\Rightarrow x=-123\)
\(\left|\left|y+1\right|-5\right|=0\Rightarrow\left|y+1\right|-5=0\Rightarrow\left|y+1\right|=5\)
\(\Rightarrow y+1=5\Rightarrow y=4\)
\(\Rightarrow y+1=-5\Rightarrow y=-6\)
