Question

Dada a função f(x) = 2x^2 – 3x + 1, calcule o valor de x para que a função f(x + 2) = 1 seja verdadeira.
A) x = -2 e x = 1/2
B) x = 2 e x = -1/2
C)x = -2 e x = -1/2
D)x = -4 e x = -9/2
E)x = -7 e x = -2/5

Answer 1

Resposta:

C)x = -2 e x = -1/2

Explicação passo a passo:

f(x) = 2x² – 3x + 1

f(x + 2) = 1

x = ?

f(x) = 2x² – 3x + 1

Para x = x + 2:

f(x + 2) = 2 . (x + 2)² – 3 . (x + 2) + 1

2 . (x² + 2 . x . 2 + 2²) – 3 . (x + 2) + 1 = 1

2 . (x² + 4x + 4) – 3x – 6 + 1 = 1

2x² + 8x + 8 – 3x – 6 = 1 – 1

2x² + 5x + 8 – 6 = 0

2x² + 5x + 2 = 0

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

x = (–5 ± √(5² – 4 • 2 • 2)) / (2 • 2)

x = (–5 ± √(25 - 16)) / 4

x = (–5 ± √9) / 4

x = (–5 ± √3²) / 4

x = (–5 ± 3) / 4

x₁ = (–5 – 3) / 4

x₁ = – (5 + 3) / 4

x₁ = – 8 / 4

x₁ = – 2

x₂ = (–5 + 3) / 4

x₂ = – (5 – 3) / 4

x₂ = – 2 / 4 ← ( / 2 )

x₂ = – 1 / 2