Đáp án:
c1 .
Ta có
`x^2/(x + y) + y^2/(y + z) + z^2/(z + x) = 2017`
`<=> (x^2 - y^2 + y^2)/(x + y) + (y^2 - z^2 + z^2)/(y + z) + (z^2 - x^2 + x^2)/(z + x) = 2017`
`<=> x - y + y^2/(x + y) + y - z + z^2/(y + z) + z - x + x^2/(z + x) = 2017`
`<=> y^2/(x + y) + z^2/(z + x) + x^2/(z + x) = 2017`
`-> y^2/(x + y) + z^2/(z + x) + x^2/(z + x) - 3 = 2017 - 3 = 2014`
c2
Ta có
`x^2/(x + y) + y^2/(y + z) + z^2/(z + x) = 2017`
`<=> (x - x^2/(x + y)) + (y - y^2/(y + z)) + (z - z^2/(z + x)) = x + y + z - 2017`
`<=> (xy)/(x + y) + (yz)/(y + z) + (zx)/(z + x) = x + y + z - 2017`
`+) 2(x + y + z) = (x + y) + (y + z) + (z + x) = (x + y)^2/(x + y) + (y + z)^2/(y + z) + (z + x)^2/(z + x)`
`= x^2/(x + y) + (2xy)/(x + y) + y^2/(x + y) + y^2/(y + z) + (2yz)/(y + z) + z^2/(y + z) + z^2/(z + x) + (2zx)/(z + x) + x^2/(z + x)`
`= (y^2/(x + y) + z^2/(z + x) + x^2/(z + x)) + (x^2/(x + y) + y^2/(y + z) + z^2/(z + x)) + 2.[ (xy)/(x + y) + (yz)/(y + z) + (zx)/(z + x) ]`
`<=> y^2/(x + y) + z^2/(z + x) + x^2/(z + x) - 3 = 2(x + y + z) - 2.[ (xy)/(x + y) + (yz)/(y + z) + (zx)/(z + x) ] - (x^2/(x + y) + y^2/(y + z) + z^2/(z + x)) - 3`
`= 2(x + y + z) - 2.[(x + y + z) - 2017] - 2017 - 3`
`= 2(x + y + z) - 2(x + y + z) + 2.2017 - 2017 - 3`
`= 2.2017 - 2017 - 3`
`= 2017 - 3`
`= 2014`
Giải thích các bước giải:
