Đáp án:
`A=5x²+5y²+8xy+2y-2x+2020`
Tách : `5x²+5y²=4x²+4y²+x²+y² `
Tách : `2020 =2018+2`
`A=(4x²+8xy+4y²)+(x²-2x+1)+(y²+2x+1)+2018`
`A=(2x+2y)²+(x-1)²+(y+1)²+2018`
`⇒A=(2x+2y)²+(x-1)²+(y+1)²≥0`
`⇒A=(2x+2y)²+(x-1)²+(y+1)²+2018>2018`
Dấu `"="` xảy ra khi :
\(\left[ \begin{array}{l}x=1\\y=1\end{array} \right.\)
Vậy `A_{max}=2018` khi \(\left[ \begin{array}{l}x=1\\y=1\end{array} \right.\)
