`***` $x²+3x-1$
$=x²+2.x.\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{13}{4}$
$=(x+\dfrac{3}{2})²-\dfrac{13}{4}$
Vì $x(+\dfrac{3}{2})²≥0$
$→(x+\dfrac{3}{2})²-\dfrac{13}{4}≥-\dfrac{13}{4}$
$→$ Dấu "=" xảy ra khi $x+\dfrac{3}{2}=0$
$→x=-\dfrac{3}{2}$
$→\min B=-\dfrac{13}{4}$ khi $x=-\dfrac{3}{2}$
`***` $-2x²+3x+1$
$=-(2x²-3x-1)$
$=-2(x²-\dfrac{3}{2}x-\dfrac{1}{2})$
$=-2(x²-2.x.\dfrac{3}{4}+\dfrac{9}{16}-\dfrac{17}{16})$
$=-2(x-\dfrac{3}{4})²+\dfrac{17}{8}$
Vì $-2(x-\dfrac{3}{4})²≤0$
$→-2(x-\dfrac{3}{4})²+\dfrac{17}{8}≤\dfrac{17}{8}$
$→$ Dấu "=" xảy ra khi $x-\dfrac{3}{4}=0$
$→x=\dfrac{3}{4}$
$→\max B=\dfrac{17}{8}$ khi $x=\dfrac{3}{4}$
