Question

Answer 1

ĐKXĐ: x>=1

\(\sqrt{x+2\sqrt{x-1}}=2x-1\)

=>\(\sqrt{x-1+2\sqrt{x-1}+1}=2x-1\)

=>\(\left|\sqrt{x-1}+1\right|=2x-1\)

=>\(\sqrt{x-1}+1=2x-1\)

=>\(\sqrt{x-1}=2x-2\)

=>\(\left\{{}\begin{matrix}x>=1\\\left(2x-2\right)^2=\left(x-1\right)\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=1\\4x^2-8x+4-x+1=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=1\\4x^2-9x+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=1\\\left(x-1\right)\left(4x-5\right)=0\end{matrix}\right.\)

=>x=1(nhận) hoặc x=5/4(nhận)