`a)`
`x^2 - 4x+ 10`
`= (x^2 - 4x + 4) + 6`
` = (x^2 - 2 . x . 2 +2^2) + 6`
` = (x-2)^2+ 6`
`\forall x` ta có :
`(x-2)^2 \ge 0`
`=> (x-2)^2 + 6 \ge 6`
`=> x^2 - 4x+10\ge 6`
Dấu `=` xảy ra `<=>x-2=0`
`<=>x=2`
Vậy `\text{Min}_{x^2 -4x+10} = 6 <=> x=2`
`b)`
`2x^2 - 6x - 20`
`= 2 (x^2 - 3x + 9/4) -49/2`
`= 2 [ x^2 - 2 . x . 3/2 + (3/2)^2] - 49/2`
` = 2 (x-3/2)^2 -49/2`
`\forall x` ta có :
`(x-3/2)^2 \ge 0`
`=> 2 (x-3/2)^2 \ge 0`
`=> 2 (x-3/2)^2 - 49/2 \ge -49/2`
`=> 2x^2 - 6x - 20 \ge -49/2`
Dấu `=` xảy ra `<=>x-3/2=0`
`<=>x=3/2`
Vậy `\text{Min}_{2x^2 - 6x-20} = -49/2 <=> x =3/2`
