ĐKXĐ: \(x\ge\frac{2016}{2017}\)
\(x^2+2015x-2014=2\sqrt{2017x-2016}\)
\(\Leftrightarrow x^2+2017x-2x-2016+1+1=2\sqrt{2017x-2016}\)
\(\Leftrightarrow\left(x^2-2x+1\right)+\left[\left(2017x-2016\right)-2\sqrt{2017x-2016}+1\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2+\left(\sqrt{2017x-2016}-1\right)^2=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-1\right)^2=0\\\left(\sqrt{2017x-2016}-1\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\\sqrt{2017x-2016}-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\\sqrt{2017x-2016}=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\2017x-2016=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\2017x=2017\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=1\end{cases}}}\)
Hay : x = 1 (tm ĐKXĐ)
=.= hok tốt!!
