D= 5x^2+8xy+5y^2-2x+2y
=4x^2+8xy+4y^2-2x+2y+y^2+x^2
=(2x+2y)^2+x^2-2*1/2x+1/4+y^2+2*1/2y+1/4-1/2
(2x+2y)^2+(x-1/2)^2+(y+1/2)^2-1/2>=-1/2
suy ra D>=-1/2 nên D có GTNN là -1/2
Ta có : 5D = 25x2 + 40xy + 25y2 - 10x + 10y
5D = (5x+ 4y - 1)2 + 9y2 + 18y - 1
5D = ( 5x + 4y - 1)2 + 9 (y + 1)2 - 2
D =\(\frac{1}{5}\). ( 5x + 4y - 1)2 + \(\frac{9}{5}\).( y + 1)2 - \(\frac{2}{5}\) \(\ge\)\(\frac{-2}{5}\)
Dấu "=" xảy ra khi y+1 = 0 \(\Leftrightarrow\)y = -1
5x + 4y - 1 = 0 \(\Leftrightarrow\)x=1
Vậy GTNN của D = \(\frac{-2}{5}\)khi x = 1 ; y = -1
Ta có: 2E = 4x2 + 8y2 - 8xy - 8x - 8y + 4006
2E = ( 4y - x - 1)2 + x2 - 6x + 4003
2E = ( 4y - x - 1)2 + ( x - 3)2 + 4003 - 9
E = \(\frac{1}{2}\).( 4y - x - 1)2 +\(\frac{1}{2}\).( x - 3 )2 + 1997 \(\ge\)1997
Dấu "=" xảy ra khi x - 3 = 0 \(\Leftrightarrow\)x = 3
4x - x -1 = 0 \(\Leftrightarrow\)y = 1
Vậy GTNN của E = 1997 khi x = 3 ; y = 1
