\(\sqrt{4x+1}-\sqrt{3x+4}=1\)
\(\Leftrightarrow\sqrt{4x+1}=1+\sqrt{3x+4}\)
\(\Leftrightarrow\left(\sqrt{4x+1}\right)^2=\left(1+\sqrt{3x+4}\right)^2\)
\(\Leftrightarrow4x+1=1+2\sqrt{3x+4}+3x+\text{4}\)
\(\Leftrightarrow-2\sqrt{3x+4}+1-1=3x-4x+4\)
\(\Leftrightarrow\left(-2\sqrt{3x+\text{4}}\right)^2=\left(-x+\text{4}\right)^2\)
\(\Leftrightarrow4\left(3x+4\right)=16-8x+x^2\)
\(\Leftrightarrow12x+16=16-8x+x^2\)
\(\Leftrightarrow12x+8x-x^2=-16+16\)
\(\Leftrightarrow20x-x^2=0\)
\(\Leftrightarrow x\left(20-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\20-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(lo\text{ại}\right)\\x=20\left(nh\text{ậ}n\right)\end{matrix}\right.\)
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