a) ĐK: \(x\le-2\)
\(x+2+\sqrt{x^2+x+2}=0\)
\(\Leftrightarrow\sqrt{x^2+x+2}=-x-2\)
\(\Leftrightarrow x^2+x+2=\left(-x-2\right)^2\)
\(\Leftrightarrow x^2+x+2=x^2+4x+4\)
\(\Leftrightarrow3x+2=0\)
\(\Leftrightarrow x=\frac{-2}{3}\)( không thỏa ĐK )
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b) ĐK: \(x\ge\frac{-1}{3}\)
\(\sqrt{x^2+3x+4}-3x=1\)
\(\Leftrightarrow\sqrt{x^2+3x+4}=3x+1\)
\(\Leftrightarrow x^2+3x+4=9x^2+6x+1\)
\(\Leftrightarrow8x^2+3x-3=0\)
\(\Leftrightarrow8\left(x^2+\frac{3}{8}x-\frac{3}{8}\right)=0\)
\(\Leftrightarrow x^2+2\cdot x\cdot\frac{3}{16}+\frac{9}{256}-\frac{105}{256}=0\)
\(\Leftrightarrow\left(x+\frac{3}{16}\right)^2=\frac{105}{256}=\left(\frac{\pm\sqrt{105}}{16}\right)^2\)
\(\Leftrightarrow x=\frac{\pm\sqrt{105}-3}{16}\)( thỏa ĐK )
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