Question

esolva por trinomio quadrado perfeito as seguintes equaçoes

a) x²+4x-21=0
b) x²-4x-12=0
c) 4x²-8x-12=0
d)) 9y²-3y-2=0

Answer 1

a) x² + 4x - 21 = 0

(x + 7).(x - 3) = x² - 3x + 7x - 21 = x² + 4x - 21

x + 7 = 0
x = - 7

x - 3 = 0
x = 3

R.: x = 3 e x = - 7
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b) x² - 4x - 12 = 0

(x + 2).(x - 6) = x² - 6x + 2x - 12 = x² - 4x - 12

x + 2 = 0
x = - 2

x - 6 = 0
x = 6

R.: x = - 2 e x = 6
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c) 4x² - 8x - 12 = 0

(2x - 6) (2x + 2) = 4x² + 4x - 12x - 12 = 4x² - 8x - 12

2x - 6 = 0
2x = 6
x = 6/2
x = 3

2x + 2 = 0
2x = - 2
x = -2/2
x = - 1

R.: x = - 1 e x = 3
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d)
9y² - 3y - 2 = 0

(3y + 1).(3y - 2) = 9y² - 6y + 3y - 2 = 9y² - 3y - 2

3y + 1 = 0
3y = - 1
y = - 1/3

3y - 2 = 0
3y = 2
y = 2/3

R.: y = -1/3 e y = 2/3