Giải pt: $2x+1+x\sqrt{x^2+2}+(x+1)\sqrt{x^2+2x+3}=0$

M

maxqn

$$2x + 1 + x\sqrt{x^2+2} + (x+1)\sqrt{x^2+2x + 3} = 0$$
ĐK: $x \in \mathbb{R}$
$$\begin{aligned} pt \Leftrightarrow & (x+1) + (x+1)\sqrt{(x+1)^2 + 2} = (-x) + (-x)\sqrt{(-x)^2+2} \\ \Leftrightarrow & x + 1 = -x \ \ \text{(vi } f(t) = t+t\sqrt{t^2+2} \ \text{dong bien tren} \ \mathbb{R}) \\ \Leftrightarrow & x = -\frac12 \end{aligned}$$

Vậy $x = -\frac12$
 
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