Đáp án+Giải thích các bước giải:
$a)A=( x-1 ) ( x-2 ) ( x-3 ) ( x-4 ) + 2003$
`=[(x-1)(x-4)][(x-2)(x-3)]+2003`
`=(x^2-5x+4)(x^2-5x+6)+2003`
`=(x^2-5x+5)^2-1+2003`
`=(x^2-5x+5)^2+2002`
Vì `(x^2-5x+5)^2>=0`
`=>A>=2022`
Dấu "=" xảy ra khi `x^2-5x+5=0`
`<=>x^2-5x+25/4=5/4`
`<=>(x-5/2)^2=5/4`
`<=>` \(\left[ \begin{array}{l}x=\dfrac{\sqrt5+5}{2}\\x=\dfrac{-\sqrt5+5}{2}\end{array} \right.\)
$b) B=3x^2 - 6xy + 5y^2 - y + 3x +2021$
`B=3(x^2-2xy+y^2)+2y^2+3x-y+2021`
`<=>4B=12(x-y)^2+12x-4y+8y^2+8084`
`<=>4B=12(x-y)^2+12(x-y)+8y^2+8y+8084`
`<=>4B=3[4(x-y)^2+4(x-y)+1]+2(4y^2+4y+1)+8079`
`<=>4B=3(2x-2y+1)^2+2(2y+1)^2+8079`
Vì `3(2x-2y+1)^2+2(2y+1)^2>=0`
`=>3(2x-2y+1)^2+2(2y+1)^2+8079>=8079`
`=>4B>=8079`
`=>B>=8079/4`
Dấu "=" xảy ra khi `y=-1/2,x=(2y-1)/2=-1`.
