Question

Determine os valores dos coeficientes a, b e c destas equações
a) 5x² - 7x = 0

b) x² - 4x + 2 = 0

c) (x - 3) . (x - 2) = 0

d) x² - 1 = 0

e) (x - 2)² = (2x - 1)²

f) 2 (x + 3) + (x + 2)² = (2x + 2)²​

Answer 1

Resposta:

a) 5x² - 7x = 0

a = 5, b = -7, c = 0

b) x² - 4x + 2 = 0

a = 1, b = -4, c = 2

c) (x - 3) . (x - 2) = 0

${x}^{2} - 2x - 3x + 6 = 0 \\ {x}^{2} - 5x + 6 = 0$

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

d) x² - 1 = 0

a = 1, b = 0, c = -1

e) (x - 2)² = (2x - 1)²

${(x - 2)}^{2} = {(2x - 1)}^{2} \\ {x}^{2} - 4x + 4 = 4 {x}^{2} - 4x + 1 \\ {x}^{2} - 4x + 4 - 4 {x}^{2} + 4x - 1 = 0 \\ - 3 {x}^{2} + 3 = 0$

a = -3, b = 0, c = 3

f) 2 (x + 3) + (x + 2)² = (2x + 2)²

$2 \times (x + 3) + {(x + 2)}^{2} = {(2x + 2)}^{2} \\ 2x + 6 + {x}^{2} + 4x + 4 = 4 {x}^{2} + 8x + 4 \\ {x}^{2} + 6x + 10 - 4 {x}^{2} - 8x - 4 = 0 \\ - 3 {x}^{2} - 2x + 6 = 0$

a = -3, b = -2, c = 6