Question

9. 8. Determine o valor de a, b e c em cada equação abaixo:

a) (x + 5) . (2x – 1) + 3x. (x – 1) = (x + 2) . (x – 2) =
b) (x + 1)2 – (x + 2)2 = (x + 1) . (x – 2)

Answer 1

Oie, Td Bom?!

a)

$(x + 5) \: . \: (2x - 1) + 3x \: . \: (x - 1) = (x + 2) \: . \: (x - 2)$

$2x {}^{2} - x + 10x - 5 + 3x {}^{2} - 3x = x {}^{2} - 4$

$5x {}^{2} + 6x - 5 = x {}^{2} - 4$

$5x {}^{2} + 6x - 5 - x {}^{2} + 4 = 0$

$4x {}^{2} + 6x - 1 = 0$

➭ $ax {}^{2} + bx + c = 0$

• Coeficientes:

$a = 4 \: ,\: b = 6 \: ,\: c = - 1$

b)

$(x + 1) {}^{2} - (x + 2) {}^{2} = (x + 1) \: . \: (x - 2)$

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

$2x + 1 - x {}^{2} - 4x - 4 = - 2x + x - 2$

$- 2x - 3 - x {}^{2} = - x - 2$

$- 2 x - 3 - x {}^{2} + x + 2 = 0$

$- x - 1 - x {}^{2} = 0$

$- x {}^{2} - x - 1 = 0$

• Multiplica tudo por - 1.

$x {}^{2} + x + 1 = 0$

➭ $ax {}^{2} + bx + c = 0$

• Coeficientes:

$a = 1 \:, \: b = 1 \: , \: c = 1$

Att. Makaveli1996