$(2)\Leftrightarrow \frac{x^{3}+x(x+1)}{x+1}=(y+2)\sqrt{(x+1)(y+1)}$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!!!