\(f\left(x\right)=x^2+2x+3\)
\(\Leftrightarrow f\left(x\right)=x^2+x+x+3\)
\(\Leftrightarrow f\left(x\right)=\left(x^2+x\right)+\left(x+3\right)\)
\(\Leftrightarrow f\left(x\right)=x\left(x+1\right)+\left(x+1\right)+3\)
\(\Leftrightarrow f\left(x\right)=\left(x+1\right)^2+3\)
Với mọi x ta có :
\(+,\left(x+1\right)^2\ge0\)
+, \(3>0\)
\(\Leftrightarrow\left(x+1\right)^2+3>0\)
\(\Leftrightarrow f\left(x\right)>0\)
\(\Leftrightarrow f\left(x\right)\) vô nghiệm
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