help mik vs dc ko mn mik vote 5s

`a, (a^2 + b^2)/2 \ge ((a + b)/2)^2`

`=> (a^2 + b^2)/2 \ge (a^2 + 2ab + b^2)/4`

`=> 4(a^2 + b^2) \ge 2(a^2 + 2ab + b^2)`

`=> 4a^2 + 4b^2 \ge 2a^2 + 4ab + 2b^2`

`=> 4a^2 + 4b^2 - 2a^2 - 4ab + 2b^2 \ge 0`

`=> 2a^2 - 4ab + 2b^2 \ge 0`

`=> 2(a^2 - 2ab + b^2) \ge 0`

`=> a^2 - 2ab + b^2 \ge 0`

`=> (a - b)^2 \ge 0`   (luôn đúng)

`=> (a^2 + b^2)/2 \ge ((a + b)/2)^2`

Dấu `"="` xảy ra `<=> (a - b)^2 = 0`

`<=> a - b = 0`

`<=> a = b`