B5:
a,
A=-x² - 4x - 2
⇔ A= - (x² + 4x +4) +2
⇔ A = 2 - (x+2)² ≤ 2
Dấu "=" xảy ra khi (x+2)² = 0 ⇒ x = -2
B = -2x² - 3x + 5
⇔ B= -(x² + 2x + 1) - (x² + x + 1/4) + 25/4
⇔ 25/4 - (x+1)² - (x+1/2)² ≤ 25/4
Dấu "=" xảy ra khi $\left \{ {{(x+1)^2=0} \atop {(x+1/2)^2=0}} \right.$
⇔ $\left \{ {{x=-1} \atop {x=-1/2}} \right.$
C = (2-x)(x+4)
⇔C= 2x + 8 - x² - 4x
⇔ C=-x² - 2x + 8
⇔ C = -(x² +2x +1) + 9
⇔ C= 9 - (x+1)² ≤ 9
Dấu "=" xảy ra khi (x+1)² = 0 ⇒ x = -1
D = 100 - 2x - x²
⇔ D = -(x² + 2x + 1) + 101
⇔D= 101 - (x+1)²) ≤101
Dấu "=" xảy ra khi (x+1)² = 0 ⇒ x = -1
E = x(1-x)
⇔E=x-x²
⇔ E = -(x² - x + 1/4) + 1/4
⇔E = 1/4 - (x - 1/2)² ≤ 1/4
Dấu "=" xảy ra khi (x-1/2)² = 0 ⇒ x = 1/2
b,
D=4x²+ 7x + 13
⇔ D= (4x² + 7x + 49/16) + 159/16
⇔ D = (2x + 7/4)² + 159/16 ≥159/16
Dấu "=" xảy ra khi (2x+7/4)²=0 ⇒ x = -7/8
E=4x² + y² - 4x + 2y + 9
⇔ E = (4x² - 4x +1) + (y² + 2y +1) + 7
⇔E = (2x-1)² + (y+1)² + 7 ≥ 7
Dấu"=" xảy ra khi $\left \{ {{(2x-1 )^2=0} \atop {(y+1)^2=0}} \right.$
⇔ $\left \{ {{2x-1=0} \atop {y+1=0}} \right.$
⇔ $\left \{ {{x=1/2} \atop {y=-1}} \right.$
