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 A=2023

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

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

Do AB//CD( vì cùng vuông góc với BD)

Nên áp dụng định lí Ta lét , ta được :

EB/ED=AB/CD

=> EB/6 = 150/4

=> EB = 150.6/4 = 225 (cm)

a) x - 3 = (3 - x)²

x - 3 = (x - 3)²

x - 3 - (x - 3)² = 0

(x - 3)[1 - (x - 3)] = 0

(x - 3)(1 - x + 3) = 0

(x - 3)(4 - x) = 0

x - 3 = 0 hoặc 4 - x = 0

*) x - 3 = 0

x = 3

*) 4 - x = 0

x = 4

Vậy x = 3; x = 4

b) x³ + 3/2 x² + 3/4 x + 1/8 = 1/64

(x + 1/2)³ = 1/64

(x + 1/2)³ = (1/4)³

x + 1/2 = 1/4

x = 1/4 - 1/2

x = -1/2