Question

Escreva as equações na forma geral e resolva a)x (x-2)=2 (x+6)
B)x (2x-1)+6=4 (x+1)
C) (x-1)(x-2)=6

Answer 1

a) x (x - 2) = 2 (x + 6)
x² - 2x = 2x + 12
x² - 2 x - 2x - 12 = 0
x² - 4x - 12 = 0

delta = b² - 4 . a . c
delta = (-4)² - 4 . 1 . (-12)
delta = 16 + 48
delta = 64

x = -b +- √ delta / 2 . a
x = - (-4) +- √64 / 2 . 1
x = 4 +- 8 / 2
x' = 4 + 8 / 2 = 12 / 2 = 6
x" = 4 - 8 / 2 = - 4 / 2 = - 2

b) x (2x - 1) + 6 = 4 (x + 1)
2x² - x + 6 = 4x + 4
2x² - x - 4x + 6 - 4 = 0
2x² - 5x + 2 = 0

delta = (-5)² - 4 . 2 . 2
delta = 25 - 16
delta = 9

x = -(-5) +- √9 / 2 . 2
x = 5 +- 3 / 4
x' = 5 + 3 / 4 = 8 / 4 = 2
x" = 5 - 3 / 4 = 2 / 4 = 1 / 2 ou 0,5

c) (x - 1) . (x - 2) = 6
x² - 2x - x + 2 = 6
x² - 2x - x + 2 - 6 = 0
x² - 3x - 4 = 0

delta = (-3)² - 4 . 1 . (-4)
delta = 9 + 16
delta = 25

x = -(-3) +- √25 / 2 . 1
x = 3 +- 5 / 2
x' = 3 + 5 / 2 = 8 / 2 = 4
x" = 3 - 5 / 2 = - 2 / 2 = - 1