ĐK:............BPT ⇔2√x+3+√19−3x+2√x+3≥x2+2x+9⇔√19−3x+4√x+3≥x2+2x+9$\Leftrightarrow (\sqrt{19-3x}-\frac{13-x}{3})+4(\sqrt{x+3}-\frac{x+5}{3})\geq x^2+2x-2⇔(−x2−x+2)9(√19−3x+(13−x3)2)+4(−x2−x+2)9(√x+3+(x+53)2)≥x2+x−2\Leftrightarrow (x^2+x-2).f(x)\leq 0Luôn có f(x)>0$$\rightarrow -2\leq x\leq 1./$
ĐK:............BPT
\Leftrightarrow 2\sqrt{x+3}+\sqrt{19-3x}+2\sqrt{x+3}\geq x^2+2x+9\Leftrightarrow \sqrt{19-3x}+4\sqrt{x+3}\geq x^2+2x+9\Leftrightarrow (\sqrt{19-3x}-\frac{13-x}{3})+4(\sqrt{x+3}-\frac{x+5}{3})\geq x^2+x-2\Leftrightarrow \frac{(-x^2-x+2)}{9(\sqrt{19-3x}+(\frac{13-x}{3})^2)}+\frac{4(-x^2-x+2)}{9(\sqrt{x+3}+(\frac{x+5}{3})^2)}\geq x^2+x-2\Leftrightarrow (x^2+x-2).f(x)\leq 0Luôn có
f(x)>0\rightarrow -2\leq x\leq 1./