Question

Resolva em C as equações:

a) x² + 100 = 0

b) x² + 2x + 2 = 0

c) x² + 16 = 0

d) x² + 4x + 5 = 0

Answer 1

Explicação passo-a-passo:

Lembrando que i² = - 1

(√i²) = i >> elimina a raíz

a) x² + 100 = 0

x² = - 100

x = √-100

x = √(-1).100

x = √-1.√100

x = √i².10

x = i.10

x = ± 10i

x' = + 10i ; x" = - 10i

S = {10i ; - 10i}

b) x² + 2x + 2 = 0

x = - b ± √b² - 4ac/2a

x = - 2 ± √(-2)² - 4.1.2/2.1

x = - 2 ±√4 - 8/2

x = - 2 ± √-4/2

x = - 2 ± √(-1).4/2

x = - 2 ± √-1.√4/2

x = - 2 ± √i².2/2

x = - 2 ± i.2/2

x = - 2 ± 2i/2

x' = -2+2i/2 = -1+i

x" = -2-2i/2 = -1-i

S = {- 1 + i ; - 1 - i}

c) x² + 16 = 0

x² = - 16

x = √-16

x = √(-1).16

x = √-1.√16

x = √i².4

x = i.4

x = ± 4i

x' = + 4i ; x" = - 4i

S = {4i ; - 4i}

d) x² + 4x + 5 = 0

x = - b ± √b² - 4ac/2a

x = - 4 ± √4² - 4.1.5/2.1

x = - 4 ± √16 - 20/2

x = - 4 ± √-4/2

x = - 4 ± √(-1).4/2

x = - 4 ± √-1.√4/2

x = - 4 ± √i².2/2

x = - 4 ± i.2/2

x = - 4 ± 2i/2

x' = -4+2i/2 = -2+i

x" = -4-2i/2 = -2-i

S = {- 2 + i ; - 2 - i}