Question

2-Determine as raízes das equações:
a) (x + 3)2 = 1
b) (x - 5)2 = 1
c) (2x - 4)2 = 0
d) (x - 3)2 = -2x2
e) x2 - 3 = 4x + 2​

Answer 1

Explicação passo-a-passo:

a) (x + 3)2 = 1

$2x + 6 = 1 \\ 2x = 1 - 6 \\ 2x = - 5 \\ x = \frac{ - 5}{2}$

b) (x - 5)2 = 1

$2x - 10 = 1 \\ 2x = 1 + 10 \\ 2x = 11 \\ x = \frac{11}{2}$

c) (2x - 4)2 = 0

$4x - 8 = 0 \\ 4x = 0 + 8 \\ x = \frac{8}{4} \\ x = 2$

d)(x - 3)2 = -2x2

$2x - 6 = { - 2x}^{2} \\ 2x + {2x}^{2} = + 6 \\ 4 {x}^{2} = 6 \\ {x}^{2} = \frac{6}{4} \\simplifica \: por \: 2 \\ {x}^{2} = \frac{ {3}^{2} }{ {2}^{2} } \\ x = \frac{9}{4}$

e) x2 - 3 = 4x + 2