Question

Resolva as equações a seguir:
(2x+3) . (2x-3) = -9 + 2x
3 . (x+2) . (x-2) = -12 + (x-4) . 2x
(x-5) . (2x-1) = 5​

Answer 1

Resposta:

a) x1=0 x2=1/2

b) x1=-8 x2=0

c) x=15/2

Explicação passo-a-passo:

a)

$4 {x}^{2} - 9 = - 9 + 2x \\ 4 {x}^{2} = 2x \\ 2 {x}^{2} - x = 0 \\ x \times (2x - 1) = 0 \\ x = 0 \\ 2x - 1 = 0 \\ x1 = 0 \\ x2 = \frac{1}{2}$

b)

$3 \times (x + 2) \times (x - 2) = - 12 + (x - 4) \times 2x \\ 3 \times ( {x}^{2} - 4) = - 12 + 2{x}^{2} - 8x \\ 3 {x}^{2} = 2 {x}^{2} - 8x \\ 3 {x}^{2} - 2 {x}^{2} + 8x = 0 \\ {x}^{2} + 8x = 0 \\ x \times (x + 18) = 8 \\ x = 0 \\ x + 8 = 0 \\ x = 0 \\ x = - 8 \\ x1 = - 8x \\ x2 = 0$

c)

$(x - 5) \times (2 \times 1) = 5 \\ (x - 5) \times 2 = 5 \\ 2x - 10 = 5 \\ 2x = 5 + 10 \\ 2x = 15 \\ x = \frac{15}{2}$