a/ Đặt $5-8x-x^2=A$
$A\,=5-8x-x^2\\\quad =-x^2-8x-16+21\\\quad =-(x^2+8x+16)+21\\\quad =-(x+4)^2+21$
Nhận thấy: $(x+4)^2\ge 0$
$↔-(x+4)^2\le 0\\↔-(x+4)^2+21\le 21\\↔A\le 21\\→\max A=21$
$→$ Dấu "=" xảy ra khi $x+4=0$
$↔x=-4$
Vậy $\max A=21$ khi $x=-4$
b/ Đặt $5-x^2+2x-4y^2-4y=B$
$B\,=5-x^2+2x-4y^2-4y\\\quad =(-x^2+2x-1)+(-4y^2-4y-1)+7\\\quad =-(x-2x+1)-(4y^2+4y+1)+7\\\quad =-(x-1)^2-(2y+1)^2+7$
Nhận thấy: $(x-1)^2\ge 0,\,(2y+1)^2\ge 0$
$↔-(x-1)^2\le 0,\,-(2y+1)^2\le 0\\↔-(x-1)^2-(2y+1)^2+7\le 7\\↔B\le 7\\→\max B=7$
$→$ Dấu "=" xảy ra khi $x-1=2y+1=0$
$↔x=1,\,2y=-1\\↔x=1,\,y=-\dfrac{1}{2}$
Vậy $\max B=7$ khi $x=1,\,y=-\dfrac{1}{2}$
