Question

Determine o conjunto solução de cada equação em C.

a) x² + 16 = 0
b) x² - 4x + 29 = 0

Answer 1

Olá Lelys,

a) x² + 16 = 0

x² = -16
x = ±√-16
x = ± 4i

b) x² - 4x + 29 = 0

Δ = (-4)² - 4.1.29
Δ = 16 - 116
Δ = -100

$x=\frac{-(-4)\pm\sqrt{-100}}{2.1}\\\\x=\frac{4+10i}{2}\\\\\boxed{x=2+5i}\\\\x'=\frac{4-10i}{2}\\\\\boxed{x=2-5i}$

Dúvidas? comente

Answer 2

a) x² +  16 = 0

Δ = b²−4ac
Δ = (0)²−4⋅1⋅16
Δ = 0 − 64
Δ = −64


x = -b ± √Δ / 2a
x = -0 ± √-64 / 2.1
x = 0 ± √64 . i / 2
x = ± 8 .i / 2
x' = - 4. i

x'' = 8 .i / 2
x'' = 4 .i

S = {-4.i,  -4.i} 

====

b) x² - 4x + 29 = 0


Δ = b²−4ac
Δ = (−4)²−4⋅1⋅29
Δ = 16 − 116
Δ = −100

x = -b ± √Δ / 2a
x = -(-4) ± √-100 / 2.1
x = 4 ± √100 . i / 2
x = 4 ± 10 .i / 2
x = 4 - 10.i /2
x' = 2 - 5.i

x'' = 4 + 10 .i / 2
x'' = 2 + 5.i


S = {2 - 5.i ,  2 + 5.i}