Question

Należy rozwiązać układ równań
v*t=24
(v+1/2)(t-1)=24

Answer 1

V*t = 24
(v+1/2)(t-1) = 24

t = 24/v
tv - v + ½t - ½ = 24

t = 24/v
24/v * v - v + ½ * 24/v - ½ = 24

t = 24/v
24 - v + 12/v - ½ = 24

t = 24/v
-v + 12/v = ½

t = 24/v
12/v = ½ + v

t = 24/v
12 = 1½ v

t = 24/v
v = 6

t = 24/6
x = 6

t = 4
v = 6

Answer 2

V*t = 24
(v+1/2)(t-1) = 24

t = 24/v
t*v - v + 1/2 t - 1/2 = 24

t = 24/v
24/v * v - v + 1/2 * 24/v - 1/2 = 24

t = 24/v
24 - v + 12/v - 1/2 - 24 = 0

t = 24/v
-v + 12/v - 1/2 = 0 / * v

t = 24/v
-v² + 12 - 0,5v = 0

liczymy deltę:
Δ = b² - 4*a*c = (-0,5)² - 4 * (-1) * 12 = 0,125 + 48 = 48,25
√Δ = 6, 94
v₁= -b -√Δ/ 2a = 0,5 - 6,94/ -2 = 3,22
v₂= -b + √Δ/ 2a = 0,5 + 6,94 = - 3,75

t ₁= 24/v₁ = 24/3,22 = 7,45
lub
t ₂ = 24/v₂= 24/ -3,75= - 6,45


v₂i t₂nie spełniają warunków równania, więc liczba v = 3,22, a t = 7,45