`(x-2019+\sqrt{(x-2019)^2+2020)}(y-2019+\sqrt{(y-2019)^2+2020})=2020`
Ta nhân `y-2019-\sqrt{(y-2019)^2+2020}` cho hai vế ta được:
`(x-2019+\sqrt{(x-2019)^2+2020})(y-2019+\sqrt{(y-2019)^2+2020})(y-2019-\sqrt{(y-2019)^2+2020})=2020(y-2019-\sqrt{(y-2019)^2+2020})`
`->(x-2019+\sqrt{(x-2019)^2+2020})[(y-2019)^2-(y-2019)^2-2020]=2020(y-2019-\sqrt{(y-2019)^2+2020})`
`->(x-2019+\sqrt{(x-2019)^2+2020})*(-2020)=2020(y-2019-\sqrt{(y-2019)^2+2020})`
`->x-2019+\sqrt{(x-2019)^2+2020})=-(y-2019)+\sqrt{(y-2019)^2+2020}(1)`
Lại có:
`(x-2019+\sqrt{(x-2019)^2+2020)}(y-2019+\sqrt{(y-2019)^2+2020})=2020`
Ta nhân `x-2019-\sqrt{(x-2019)^2+2020}` cho hai vế ta được:
`(x-2019+\sqrt{(x-2019)^2+2020})(y-2019+\sqrt{(y-2019)^2+2020})(x-2019-\sqrt{(x-2019)^2+2020})=2020(x-2019-\sqrt{(x-2019)^2+2020})`
`->(y-2019+\sqrt{(y-2019)^2+2020})[(x-2019)^2-(x-2019)^2-2020]=2020(x-2019-\sqrt{(x-2019)^2+2020})`
`->(y-2019+\sqrt{(y-2019)^2+2020})*(-2020)=2020(x-2019-\sqrt{(x-2019)^2+2020})`
`->y-2019+\sqrt{(y-2019)^2+2020})=-(x-2019)+\sqrt{(x-2019)^2+2020}(2)`
Lấy `(1)+(2)` theo vế ta được:
`(x-2019+\sqrt{(x-2019)^2+2020})+(y-2019+\sqrt{(y-2019)^2+2020})=-(x-2019)+\sqrt{(x-2019)^2+2020}-(y-2019)+\sqrt{(y-2019)^2+2020}`
`->(x-2019)+(y-2019)=-(x-2019)-(y-2019)`
`->x-2019+y-2019=-x+2019-y+2019`
`->x+y+x+y=2019+2019+2019+2019`
`->2(x+y)=4*2019`
`->x+y=2*2019=4038`
Vậy: `A=x+y=4038`
