Question

TÌm Min và Max:

A= (x+1)² + (x+2)²

B= -2x² - 4

C= -5x² + 10x - 7

D= x² + 2y² + 2xy - y + 1

E= 2x² - 4x - 2xy + y² - 1

F= (1-x) . (x+2) . (x+3) . (x+6)

G= x² + xy

Answer 1

\(A=\left(x+1\right)^2+\left(x+2\right)^2=\left(x+1\right)^2+\left(-2-x\right)^2\ge\frac{1}{2}\left(x+1-2-x\right)^2=\frac{1}{2}.1^2=\frac{1}{2}\Rightarrow A_{min}=\frac{1}{2}\Leftrightarrow x=\frac{3}{2}\)

\(B=-2x^2-4\le0-4=-4\Rightarrow B_{max}=-4\Leftrightarrow x=0\)

\(C=-5x^2+10x-7=-5x^2+10x-5-2=-5\left(x-1\right)^2-2\le0-2=-2\Rightarrow C_{min}=-2\Leftrightarrow x-1=0\Leftrightarrow x=1\)