`2(x+1)^2+3(x+2)^2-4(x+3)^2`
`=2x^2+4x+2+3x^2+12x+12-4x^2-24x-36`
`=x^2-8x-22`
`=x^2-2.x.4+16-38`
`=(x-4)^2-38`
Vì `(x-4)^2 >= 0 AA x`
`<=>(x-4)^2-38 >= -38 AA x`
Hay `2(x+1)^2+3(x+2)^2-4(x+3)^2 >= -38 AA x`
Dấu "`=`" xảy ra `<=>(x-4)^2=0<=>x=4`
Vậy `GTN N` của bt là `-38` khi `x=4`
\(A=2\left(x+1\right)^2+3\left(x+2\right)^2-4\left(x+3\right)^2\)
\(=2\left(x^2+2x+1\right)+3\left(x^2+4x+4\right)-4\left(x^2+6x+9\right)\)
\(=2x^2+4x+2+3x^2+12x+12-4x^2-24x-36\)
\(=x^2-8x-22=\left(x-4\right)^2-38\ge-38\)
Dấu "=" xảy ra \(\Leftrightarrow\left(x-4\right)^2=0\Leftrightarrow x=4\)
Vậy \(MinA=-38\)
