`\color{#274e13}{♡}\color{#38761d}{C}\color{#55953a}{h}\color{#79b95d}{a}\color{#98d97c}{n}\color{#b7fa99}{h}`

Ta có `:`

`(x - y)^2 ge 0 AA x, y`

`to x^2 - 2 . x . y + y^2 ge 0`

`to x^2 + y^2 ge 2 . x . y`

`to 2(x^2 + y^2) ge x^2 + 2 . x . y + y^2`

`to 2(x^2 + y^2) ge (x + y)^2`

`to 2 . 2 ge A^2`

`to A^2 le 4`

`to A le 2 (` vì `x > 0, y > 0)`

Dấu "`=`" xảy ra khi `:`

`{(x = y),(x^2 + y^2 = 2):}`

`to 2 . x^2 = 2`

`to x^2 = 1`

`to x = 1 (tmđk)`

`to y = 1 (tmđk)`

Vậy `max A = 2` khi `x = 1, y = 1.`