Câu 15:
1: Ta có: \(\sqrt{2x+5}=\sqrt{1-x}\)
\(\Leftrightarrow2x+5=1-x\)
\(\Leftrightarrow2x+x=1-5\)
\(\Leftrightarrow3x=-4\)
hay \(x=-\dfrac{4}{3}\)
2: Ta có: \(\sqrt{2x-1}=\sqrt{x-1}\)
\(\Leftrightarrow2x-1=x-1\)
\(\Leftrightarrow x=0\)(loại
3: Ta có: \(\sqrt{x^2-x}=\sqrt{3x-5}\)
\(\Leftrightarrow x^2-x=3x-5\)
\(\Leftrightarrow x^2-4x+5=0\)
\(\Leftrightarrow\left(x-2\right)^2+1=0\)(vô lý
4: Ta có: \(\sqrt{2x^2-3}=\sqrt{4x-3}\)
\(\Leftrightarrow2x^2=4x\)
\(\Leftrightarrow2x^2-4x=0\)
\(\Leftrightarrow2x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=2\left(nhận\right)\end{matrix}\right.\)
5: Ta có: \(\sqrt{x^2-x}=\sqrt{3-x}\)
\(\Leftrightarrow x^2=3\)
\(\Leftrightarrow x\in\left\{\sqrt{3};-\sqrt{3}\right\}\)