(2)\Leftrightarrow \frac{x^{3}+x(x+1)}{x+1}=(y+2)\sqrt{(x+1)(y+1)}Chia 2 vế cho \sqrt{x+1} :\Leftrightarrow (\frac{x}{\sqrt{x+1}})^{3}+\frac{x}{\sqrt{x+1}}=(\sqrt{y+1})^{3}+\sqrt{y+1}f(t)= t^{3}+t f'(t)= 3t^{2}+1>0 \forall t \in R\Rightarrow f(\frac{x}{\sqrt{x+1}})=f(\sqrt{y+1})\Leftrightarrow \frac{x}{\sqrt{x+1}}=\sqrt{y+1}bạn tự giải nha!!!
$(2)\Leftrightarrow \frac{x^{3}+x(x+1)}{x+1}=(y+2)\sqrt{(x+1)(y+1)}
$Chia 2 vế cho
$ \sqrt{x+1}
$:
$\Leftrightarrow (\frac{x}{\sqrt{x+1}})^{3}+\frac{x}{\sqrt{x+1}}=(\sqrt{y+1})^{3}+\sqrt{y+1}
$$f(t)= t^{3}+t
$$f'(t)= 3t^{2}+1>0 \forall t \in R
$$\Rightarrow f(\frac{x}{\sqrt{x+1}})=f(\sqrt{y+1})
$$\Leftrightarrow \frac{x}{\sqrt{x+1}}=\sqrt{y+1}
$bạn tự giải nha!!!