\(x^2+3x+1=\left(x+3\right)\sqrt{x^2+1}\)
\(\Rightarrow x^2+3x+1-x\sqrt{x^2+1}-3\sqrt{x^2+1}=0\)
\(\Rightarrow\sqrt{x^2+1}\left(\sqrt{x^2+1}-3\right)-x\left(\sqrt{x^2+1}-3\right)=0\)
\(\Rightarrow\left(\sqrt{x^2+1}-3\right)\left(\sqrt{x^2+1}-x\right)=0\)
Xét \(\sqrt{x^2+1}-3=0\)
\(\Rightarrow x^2+1=9\)
\(\Rightarrow x=\pm2\sqrt{2}\)
Xét \(\sqrt{x^2+1}-x=0\)
\(\Rightarrow x^2+1=x^2\)
\(\Rightarrow1=0\) ( vô lí )
Vậy nghiệm của pt là \(x=\pm2\sqrt{2}\)
x2+3x+1=(x+3)√x2+1x2+3x+1=(x+3)x2+1
⇒x2+3x+1−x√x2+1−3√x2+1=0⇒x2+3x+1−xx2+1−3x2+1=0
⇒√x2+1(√x2+1−3)−x(√x2+1−3)=0⇒x2+1(x2+1−3)−x(x2+1−3)=0
⇒(√x2+1−3)(√x2+1−x)=0⇒(x2+1−3)(x2+1−x)=0
Xét √x2+1−3=0x2+1−3=0
⇒x2+1=9⇒x2+1=9
⇒x=±2√2⇒x=±22
Xét √x2+1−x=0x2+1−x=0
⇒x2+1=x2⇒x2+1=x2
⇒1=0⇒1=0 ( vô lí )
Vậy nghiệm của pt là x=±2√2
