Question

Tìm Min:

a) A= 2x² +2xy +y² - 2x +2y +2

b) B= x² + xy + y²- 3x - 3y

Answer 1

\(A=\left(y^2+2y\left(x+1\right)+\left(x+1\right)^2\right)+\left(2x^2-2x+2-\left(x+1\right)^2\right)\)

\(=\left(y+x+1\right)^2+\left(x-2\right)^2-3\ge-3\)

Min A=-3 khi x=2;y=-3

Answer 2

\(B=\left(x^2+x\left(y-3\right)+\frac{\left(y-3\right)^2}{4}\right)+\left(y^2-3y-\frac{\left(y-3\right)^2}{4}\right)\)

\(=\left(x+\frac{y-3}{2}\right)^2+\frac{3\left(y^2-2y+1\right)-12}{4}\)

\(=\left(....\right)^2+\frac{3}{4}\left(y-1\right)^2-3\ge3\)

Min B=-3 khi y=1;x=1

Answer 3

Answer 4

b) nhân 2 vế với 2 cho dễ làm

Answer 5

B= -3 nhé