Giúp e nhanh nha , pls …

Giải thích các bước giải:

Ta có: 

$2\cdot (\dfrac{x}y+\dfrac yx)+(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2})\ge 2\sqrt{\dfrac xy.\dfrac yx}+2\sqrt{\dfrac{x^2}{y^2}.\dfrac{y^2}{x^2}}$

$\to 2\cdot (\dfrac{x}y+\dfrac yx)+(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2})\ge 6$

$\to 1+\dfrac{2y}x+\dfrac{y^2}{x^2}+\dfrac{x^2}{y^2}+1+\dfrac{2x}y\ge 8$

$\to \dfrac{x^2+2xy+y^2}{x^2}+\dfrac{x^2+y^2+2xy}{y^2}\ge 8$

$\to \dfrac{(x+y)^2}{x^2}+\dfrac{(x+y)^2}{y^2}\ge 8$

$\to \dfrac1{x^2}+\dfrac1{y^2}\ge \dfrac8{(x+y)^2}$