cho x^2/(x+y) + y^2/(y+z) + z^2/(z+x) = 2017. tinhs y^2/(x+y) + z^2/(y+z) + x^2/(z+x) -3

#LC

Có `x^2/(x+y)+y^2/(y+z)+z^2/(z+x)=2017`

Xét

`(x^2/(x+y) + y^2/(y+z) + z^2/(z+x))-(y^2/(x+y) + z^2/(y+z) + x^2/(z+x))`

`= (x^2-y^2)/(x+y)+(y^2-z^2)/(y+z)+(z^2-x^2)/(x+z)`

`= ((x-y)(x+y))/(x+y) +((y-z)(y+z))/(y+z)+((z-x)(x+z))/(x+z)`

`=x-y+y-z+z-x`

`=0`

`=> y^2/(x+y) + z^2/(y+z) + x^2/(z+x) =x^2/(x+y) + y^2/(y+z) + z^2/(z+x)  =2017`

`=> y^2/(x+y) + z^2/(y+z) + x^2/(z+x) - 3=2017-3=2014`