Cái pt (1)

$x^3+y^3=(x+y)(x^2+y^2-xy)=(x+y)(x^2+y^2)-xy(x+y)$
$\geq (x+y)(x^2+y^2)-xy\sqrt{2(x^2+y^2)} =\sqrt{2(x^2+y^2)}((x+y)\sqrt{\frac{x^2+y^2}{2}})-xy)\geq xy\sqrt{2(x^2+y^2)}$
Dấu = khi x=y
Thế vào pt dưới .
chú ý $2x+2\sqrt{(x-1)(x+1)}=(\sqrt{x+1} +\sqrt{x-1})^2$
pt $\iff 2(\sqrt{x+1}+\sqrt{x-1})=9\sqrt{x-1}(x-1)$
$\iff 2\sqrt{x+1}=\sqrt{x-1}(9x-11) \iff (3x-5)(27x^2-48x+25)=0$