Question

1.Utilizando o método da fatoração, determine as raízes das equações:
a) x² - 4x + 4 = 9
b) x² + 12x + 36 = 0
c) 4x² - 12x + 9 = 1
d) x² + 2x – 8 = 0

Answer 1

Oie, tudo bom?

a) x² - 4x + 4 = 9

x² - 4x + 4 - 9 = 0

x² + x - 5x - 5 = 0

x . (x + 1) - 5(x + 1) = 0

(x + 1) . (x - 5) = 0

x + 1 = 0 x = - 1

x - 5 = 0 x = 5

S = {- 1 , 5}

b) x² + 12x + 36 = 0

x² + 2 . x . 6 + 6² = 0

(x + 6)² = 0

x + 6 = 0 x = - 6

S = {- 6}

c) 4x² - 12x + 9 = 1

4x² - 12x + 9 - 1 = 0

4x² - 12x + 8 = 0

[4x² - 12x + 8]/4 = 0

x² - 3x + 2 = 0

x² - x - 2x + 2 = 0

x . (x - 1) - 2(x - 1) = 0

(x - 1) . (x - 2) = 0

x - 1 = 0 x = 1

x - 2 = 0 x = 2

S = {1 , 2}

d) x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x . (x + 4) - 2(x + 4) = 0

(x + 4) . (x - 2) = 0

x + 4 = 0 x = - 4

x - 2 = 0 x = 2

S = {- 4 , 2}

Att. NLE Top Shotta