1.
`a,-x^2-2x-3`
`=-x^2-3x-1-2`
`=-(x+1)^2-2<0∀x`
`b,-x^2+8x-20`
`=-x^2+8x-16-4`
`=-(x-4)^2-4<0∀x`
`c)-4x^2+4x-3`
`=-4x^2+4x-1-2`
`=-(2x-1)^2-2<0∀x`
2.
`M=x^2-4x+7`
`=x^2-4x+4+3`
`=(x+2)^2+3\geq3`
Dấu bằng xảy ra khi `x=-2`
`P=2x^2-6x`
`=2x^2-6x+9/2-9/2`
`=2(x^2-3x+9/4)-9/2`
`=2(x-3/2)^2-9/2\geq-9/2`
Dấu bằng xảy ra khi x=3/2
`A=(x^2+1)^2+4\geq4`
Dấu bằng xảy ra khi x^2+1=0
`=>x^2=-1`(vô lý)
=> không có x để A min
`S=x^2+y^2-6x+2x+89`
`=(x^2-4x+4)+y^2+85`
`=(x-2)^2+y^2+85\geq85`
Dấu bằng xảy ra khi
$\left \{ {{y=0} \atop {x=2}} \right.$
`G=2x^2+4y^2-4xy+2x+101`
`=2(x^2-2xy+y^2)+2y^2+101`
`=2(x-y)^2+2y^2+101\geq101`
Dấu bằng xảy ra khi x=y=0
`T=x^4-7x^2-4x+20440`
`=x^4-2x^3+2x^3-4x^2-3x^2+6x-10x+20+20420`
`=(x-2)^2(x^2+4x+5)+20420\geq20420`(Do `x^2+4x+5>0`)
Dấu bằng xảy ra khi x=2
