`(x + 1)(x + 4) - 3\sqrt{x^2+5x+2}=6`
`⇔x^2 + 4x + x + 4 - 3\sqrt{x^2+5x+2}=6`
`⇔x^2 + 5x + 2 + 2 - 3\sqrt{x^2+5x+2}=6`
`⇔x^2 + 5x + 2 - 3\sqrt{x^2+5x+2} = 4`
`⇔\sqrt{x^2+5x+2}(\sqrt{x^2+5x+2}-3)=4`
$\text{Gọi: $\sqrt{x^2+5x+2}$ là y (y ≥ 0)}$
`⇒ y(y - 3) = 4`
`⇔ y^2 - 3y - 4 = 0`
`⇔ y^2 - 4y + y - 4 = 0`
`⇔ y(y - 4) + (y - 4) = 0`
`⇔ (y + 1)(y - 4) = 0`
`⇔` \(\left[ \begin{array}{l}y+1=0\\y-4=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}y=-1(KTM)\\y=4(TM)\end{array} \right.\)
$\text{Có: y = 4 (cmt)}$
`⇒ \sqrt{x^2+5x+2} = 4`
`⇔ x^2 + 5x + 2 = 16`
`⇔ x^2 + 5x - 14 = 0`
`⇔ x^2 + 7x - 2x - 14 = 0`
`⇔ x(x + 7) - 2(x + 7) = 0`
`⇔ (x - 2)(x + 7) = 0`
`⇔` \(\left[ \begin{array}{l}x-2=0\\x+7=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=2\\x=-7\end{array} \right.\)
$\text{Vậy tập nghiệm của pt: S = {2; -7}}$
