Question

\(\sqrt{4x^2-1}-2\sqrt{2x-1}=0\)

Answer 1

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

=>\(x>=\dfrac{1}{2}\)

\(\sqrt{4x^2-1}-2\sqrt{2x-1}=0\)

=>\(\sqrt{\left(2x-1\right)\left(2x+1\right)}-2\sqrt{2x-1}=0\)

=>\(\sqrt{2x-1}\left(\sqrt{2x+1}-2\right)=0\)

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

=>\(\left[{}\begin{matrix}x=\dfrac{1}{2}\left(nhận\right)\\x=\dfrac{3}{2}\left(nhận\right)\end{matrix}\right.\)

Answer 2

  Nếu có sai sót thì nhắc mình sửa ^^