Question

Resolva o sistema:
{a.b=16
{a+b=23

Answer 1

ab = 16
a + b = 23

a + b = 23
b = 23 - a

ab = 16
a(23 - a) = 16
23a - a² = 16
- a² + 23a - 16 = 0
a = - 1, b = 23, c = - 16

Δ = b² - 4ac
Δ = 23² - 4 . (- 1) . (- 16)
Δ = 529 - 64
Δ = 465

a = (- b ± √Δ)/2a
a = (- 23 ± √465)/2 . (- 1)
a = (- 23 ± √465)/- 2
a = (23 ± √465)/2

a' = (23 + √465)/2
a'' = (23 - √465)/2


b = 23 - a

b' = 23 - (23 + √465)/2
b'' = 23 - (23 - √465)/2


a = (23 + √465)/2, b = 23 - (23 + √465)/2
a = (23 - √465)/2, b = 23 - (23 - √465)/2