Lời giải:
Ta có: `|x+2y|^2020>=0, |y+4|^2020>=0`
`=> |x+2y|^2020 +|y+4|^2020>=0`
Dấu "=" xảy ra `<=> x+2y=0, y+4=0`
`=> x=-2y, y=-4`
`=> x=8`
Vậy `x=8, y=-4`
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`x^2+x+1`
`=(x^2+2.x. 1/2+1/4)-1/4+1`
`=(x+1/2)^2+3/4>=3/4`
`(vì (x+1/2)^2>=0 )`
Dấu "=" xảy ra `<=> x+1/2=0`
`=> x=-1/2`
Vậy GTNN`=3/4` khi `x=-1/2`