Question

preciso de ajuda nessa questão!!​

Answer 1

Resposta:

a) x' = 2 , x" = 3.

b) x' = -1/2 , x" = 1/3.

c) x = 2.

d) x∉R.

e) x = -1.

Explicação passo a passo:

a) x² - 5x + 6 = 0

a = 1 , b = -5 , c = 6

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-(-5) ± √((-5)² - 4 • 1 • 6)) / (2 • 1)

x = (5 ± √(25 - 24)) / 2

x = (5 ± √1) / 2

x = (5 ± √1²) / 2

x = (5 ± 1) / 2

x' = (5 - 1) / 2

x' = 4 / 2

x' = 2

x" = (5 + 1) / 2

x" = 6 / 2

x" = 3

b) 6x² + x - 1 = 0

a = 6 , b = 1 , c = -1

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-1 ± √(1² - 4 • 6 • (-1))) / (2 • 6)

x = (-1 ± √(1 - 4 • (-6))) / 12

x = (-1 ± √(1 + 24)) / 12

x = (-1 ± √25) / 12

x = (-1 ± √5²) / 12

x = (-1 ± 5) / 12

x' = (-1 - 5) / 12

x' = -6 / 12

x' = -1/2

x" = (-1 + 5) / 12

x" = 4 / 12

x" = 1/3

c) x² - 4x + 4 = 0

a = 1 , b = -4 , c = 4

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-(-4) ± √((-4)² - 4 • 1 • 4)) / (2 • 1)

x = (4 ± √(16 - 16)) / 2

x = (4 ± √0) / 2

x = (4 ± √0²) / 2

x = (4 ± 0) / 2

x = 4 / 2

x = 2

d) x² + 10x + 32 = 0

a = 1 , b = 10 , c = 32

Δ = 10² - 4 • 1 • 32

Δ = 100 - 128

Δ = -28      ← Δ < 0.

x∉R

e) 4x² + 8x + 4 = 0

a = 4 , b = 8 , c = 4

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-8 ± √(8² - 4 • 4 • 4)) / (2 • 4)

x = (-8 ± √(64 - 64)) / 8

x = (-8 ± √0) / 8

x = (-8 ± √0²) / 8

x = (-8 ± 0) / 8

x = -8 / 8

x = -1