Bài giải
\(\left|\sqrt{x+1}-0,5\right|-0,6=\sqrt{\left(-3\right)^2}+0,4\)
\(\left|\sqrt{x+1}-0,5\right|-0,6=3+0,4\)
\(\left|\sqrt{x+1}-0,5\right|-0,6=3,4\)
\(\left|\sqrt{x+1}-0,5\right|=3,4+0,6\)
\(\left|\sqrt{x+1}-0,5\right|=4\)
\(\Rightarrow\orbr{\begin{cases}\sqrt{x+1}-0,5=-4\\\sqrt{x+1}-0,5=4\end{cases}\Rightarrow}\orbr{\begin{cases}\sqrt{x+1}=-3,5\text{ ( loại ) }\\\sqrt{x+1}=4,5\end{cases}}\Rightarrow\text{ }x+1=20,25\text{ }\Rightarrow\text{ }x=19,25\)
\(\Rightarrow\text{ }x=19,25\)
Ta có: \(|\sqrt{x+1}-0,5|=4\)\(\left(ĐK:x\ge-1\right)\)
<=> \(\orbr{\begin{cases}\sqrt{x+1}-0,5=4\\\sqrt{x+1}-0,5=-4\end{cases}}\)
<=> \(\orbr{\begin{cases}x=19,25\\x\in\varnothing\end{cases}}\)
