A=(x2−2xy+y2)+y2+2x−6y+2028

\(= \left(\right. x - y \left.\right)^{2} + 2 \left(\right. x - y \left.\right) + \left(\right. y^{2} - 4 y \left.\right) + 2028\)

\(= \left(\right. x - y \left.\right)^{2} + 2 \left(\right. x - y \left.\right) + 1 + \left(\right. y^{2} - 4 y + 4 \left.\right) + 2023\)

\(= \left(\right. x - y + 1 \left.\right)^{2} + \left(\right. y - 2 \left.\right)^{2} + 2023 \geq 0 + 0 + 2023 = 2023\)
Vậy Amin⁡=2023Amin​=2023.

Giá trị này đạt tại \(x - y + 1 = y - 2 = 0\)

\(\Leftrightarrow y = 2 ; x = 1\)

a)Ta có: 3x(x – 1) + x – 1 = 0

⇔3x(x – 1) + (x – 1) = 0

⇔(x – 1)(3x + 1) = 0

⇔[x−1=03x+1=0⇔[x=1x=−13.
b)\(x^2-9x=0x(x-9)=0\Rightarrow[x=0x-9=0\Rightarrow[x=0x=9\)

Vậy \([x=0x=9[x=0x=9​\)

a) x2−10x+25−y2

=(x−5)2−y2

=(x−5+y)(x−5−y)

=(x+y−5)(x−y−5).

b) x3+y3−3x−3y

=(x3+y3)−(3x+3y)

=(x+y)(x2−xy+y2)−3(x+y)

=(x+y)(x2−xy+y2−3).

c) x3+2x2y+xy2−4x

=x(x2+2xy+y2)−4x
=x(x+y)2−4x

=x[(x+y)2−22]

=x(x+y+2)(x+y−2). 

a) (2x + 1) ^ 2 = 4x ^ 2 + 4x + 1

b) (a - b/2) ^ 3 = a ^ 3 - 3a ^ 2 * b/2 + 3a * (b/2) ^ 2 - (b/2) ^ 3 = a³-3a²b+ab²-63.