a. Jika x1 dan x2 akar-akar persamaan 4x + ax + a = 8 ,hitunglah minimum dari (x1 - x2 )² B. Diberikan 2x + y = 20 dan R = x.y tentukanlah nilai R maksimum

nilai minimum

4x² + ax  + a = 8
4x² + ax + a - 8 = 0
x1 + x2 = -a/4
x1 x 2 = (a - 8)/4

(x1 - x2)² = (x1 + x2)² - 4 x1x2
(x1 - x2)²  =(-a/4)² - 4(a-8)/4
(x1 - x2)² = a²/16 - (a - 8)
misal (x1 - x2)²  = p
p = 1/16 a² - a + 8
p'(a)= 0
1/8 a - 1 = 0
1/8  a = 1
a = 8
p = 1/16 a² - a + 8
p = 1/16(8²)  - 8 +8
p = 1/16 (64)=  4
nilai min (x1 - x2)²  = 4

b.
2x + y = 20
y = 20 - 2x

R = x.y
R = x (20 - 2x)
R(x)= 20 x - 2x²
maksimum  R'(x) = 0
20 - 4x = 0
4x = 20
x = 5
sub ke  R(x)= 20 x - 2x²
R(5) = 20(5) - 2(5²)
R(5) = 100 - 50
R(5) = 50