Đáp án+Giải thích các bước giải:
`P=2x^2+5x+1`
`P=2(x^2+5/2x)+1`
`P=2(x^2+5/2x+25/16)-25/8+1`
`P=2(x+5/4)^2-17/8>=-17/8`
Dấu "=" xảy ra khi `x=-5/4.`
`Q=x^2+y^2-4x+y+1`
`Q=x^2-4x+4+y^2+y+1/4+1-4-1/4`
`Q=(x-2)^2+(y+1/2)^2-13/4>=-13/4`
Dấu "=" xảy ra khi `x=2,y=-1/2.`
`I=5x^2+2y^2+8x+2y-2xy+4`
`=>2I=10x^2+4y^2-4xy+16x+4y+8`
`=>2I=(y-2x)^2+4y-8x+9x^2+24x+16-8`
`=>2I=(y-2x)^2+4(y-2x)+4+(3x+4)^2-12`
`=>2I=(y-2x+2)^2+(3x+4)^2-12>=-12`
`=>I>=-6`
Dấu "=" xảy ra khi `x=-4/3,y=2x-2=14/3.`