Đáp án+Giải thích các bước giải:
`A=x^2+3x-1`
`=x^2+3x+9/4-9/4-1`
`=(x^2+3x+9/4)-9/4-1`
`=[x^2+2.x.({3}/2)^2]-9/4-4/4`
`=(x+3/2)^2-13/4`
Vì `(x+3/2)^2≥0`
`=>(x+3/2)^2-13/4≥-13/4`
`=>A≥-13/4`
Vậy `min` `A=-13/4` `<=>x+3/2=0=>x=-3/2`
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`B=5x^2+10x-2020`
`=5x^2+10x+5-5-2020`
`=(5x^2+10x+5)-5-2020`
`=5(x^2+2x+1)-2025`
`=5(x^2+2.x.1+1^2)-2025`
`=5(x+1)^2-2025`
Vì `(x+1)^2≥0`
`=>5(x+1)^2≥0`
`=>5(x+1)^2-2025≥-2025`
`=>B≥-2025`
Vậy `min` `B=-2025` `<=>x+1=0=>x=-1`
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`C=4x^2+5x+y^2-2y+2019`
`=4x^2+5x+5/4+y^2-2y+1-1-5/4+2019`
`=(4x^2+5x+25/16)+(y^2-2y+1)-1-25/16+2019`
`=[(2x)^2+2.2x.{5}/4+(5/4)^2]+(y^2-2.y.1+1^2)+32263/16`
`=(2x+5/4)^2+(y+1)^2+32263/16`
Vì `(2x+5/4)^2≥0`
`(y+1)^2≥0`
`=>(2x+5/4)^2+(y+1)^2≥0`
`=>(2x+5/4)^2+(y+1)^2+32263/16≥32263/16`
`=>C≥32263/16`
Dấu `=` xảy ra khi:
`{((2x+5/4)^2=0),((y-1)^2=0):}<=>{(2x+5/4=0),(y-1=0):}<=>{(2x=-5/4),(y=1):}<=>{(x=-5/8),(y=1):}`
Vậy `min` `C=32263/16` khi `x=-5/8` và `y=1`
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`D=1/2-7x+25x^2`
`=49/100-7x+25x^2-49/100+1/2`
`=(49/100-7x+25x^2)-49/100+1/2`
`=[(7/10)^2-2.{7}/{10}.5x+(5x)^2]-49/100+50/100`
`=(7/10-5x)^2+1/100`
Vì `(7/10-5x)^2≥0`
`=>(7/10-5x)^2+1/100≥1/100`
`=>D≥1/100`
Vậy `min` `D=1/100` `<=>7/10-5x=0=>5x=7/10=>x=7/50`
