Đáp án:
Giải thích các bước giải:
`(\sqrt{x+8}-\sqrt{x+3})(\sqrt{x^2+11x+24}+1)=5`
ĐKXĐ: `x \ge -3`
`⇔ (\sqrt{x+8}-\sqrt{x+3})(\sqrt{x^2+11x+24}+1)=(\sqrt{x+8}-\sqrt{x+3})(\sqrt{x+8}+\sqrt{x+3})`
`⇔ (\sqrt{x+8}-\sqrt{x+3})(\sqrt{x^2+11x+24}+1-\sqrt{x+8}-\sqrt{x+3})=0`
`⇔ (\sqrt{x+8}-\sqrt{x+3})(\sqrt{x+8}-1)(\sqrt{x+3}-1)=0`
`⇔` \(\left[ \begin{array}{l}\sqrt{x+8}-\sqrt{x+3}=0\\\sqrt{x+8}-1=0\\\sqrt{x+3}-1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x+8=x+3\ (VL)\\x+8=1\\x+3=1\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-7\ (L)\\x=-2\ (TM)\end{array} \right.\)
Vậy `S={-2}`
