Đáp án + giải thích các bước giải :

`A=4x^2+12x+1` $\\$` A = (2x)^2 + 2.2x.3 + 3^2 - 8` $\\$` A = (2x+3)^2 - 8` $\\$` Vì : (2x+3)^2 ge 0 AA x => A = (2x+3)^2 - 8 ge -8 AA x` $\\$ $Min A = 8$` \Leftrightarrow 2x + 3 = 0 \Leftrightarrow 2x = -3 \Leftrightarrow x = -3/2` $\\$ `B = x^2 - 3x` $\\$` B = x^2 - 2. x . 3/2 + (3/2)^2 - 9/4` $\\$ `B = (x-3/2)^2 - 9/4` $\\$ `Vì : (x-3/2)^2 ge 0 AA x => B = (x-3/2)^2 - 9/4ge -9/4 AA x` $\\$ $Min B = -\frac{9}{4}$` \Leftrightarrow x - 3/2 = 0 \Leftrightarrow x = 3/2 ` $\\$ `C = 2x^2 + 2x +1` $\\$` C = 2(x^2 + x + 1/4) + 1/2` $\\$` C = 2(x+1/2)^2 + 1/2` $\\$` Vì : 2(x+1/2)^2 ge 0 AA x => C = 2(x+1/2)^2 + 1/2 ge 1/2 AA x ` $\\$$Min C $ ` = 1/2 \Leftrightarrow x + 1/2 = 0 \Leftrightarrow x =-1/2`

Đáp án `+` Giải thích các bước giải `!`

`to` Tìm Min:

`a)`

`A= 4x^2+12x+1`

`= (4x^2+12x+9)-8`

`= (2x+3)^2-8`

Vì `(2x+3)^2 >= 0` `AA x`

`=> (2x+3)^2-8 >= -8`

Dấu `\text{"="}` xảy ra:

`<=> (2x+3)^2 = 0`

`<=> 2x+3 = 0`

`<=> 2x = -3`

`<=> x = -(3)/2`

Vậy $Min_A$ `=-8 <=> x=-(3)/2`

`b)`

`B= x^2-3x`

`= (x^2-3x+9/4)-9/4`

`= (x-3/2)^2-9/4`

Vì `(x-3/2)^2 >= 0` `AA x`

`=> (x-3/2)^2-9/4 >= -(9)/4`

Dấu `\text{"="}` xảy ra:

`<=> (x-3/2)^2 = 0`

`<=> x-3/2 = 0`

`<=> x = 3/2`

Vậy $Min_B$ `=-(9)/4 <=> x=3/2`

`c)`

`C= 2x^2+2x+1`

`= 2(x^2+x+1/2)`

`= 2(x^2+x+1/4+1/4)`

`= 2(x+1/2)^2+1/2`

Vì `2(x+1/2)^2 >= 0` `AA x`

`=> 2(x+1/2)^2+1/2 >= 1/2`

Dấu `\text{"="}` xảy ra:

`<=> 2(x+1/2)^2 = 0`

`<=> x+1/2 = 0`

`<=> x = -(1)/2`

Vậy $Min_C$ `=1/2 <=> x=-(1)/2`