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

d) (2x - 3) (x - 8) = 34

preciso pra amanhã, conta tem q ser completa

Answer 1

a) x(x - 2) = 2(x + 6)

x² - 2x = 2x + 12

x² - 2x - 2x - 12 = 0

x² - 4x - 12 = 0

Δ = b² - 4ac

Δ = (-4)² - 4(1)(-12)

Δ = 16 + 48

Δ = 64

x = - b ± √Δ / 2a

x = 4 ± 8 / 2(1)

x' = 4 + 8 / 2

x' = 12/2

x' = 6

x'' = 4 - 8 / 2

x'' = - 4/2

x'' = - 2

S = { -2, 6 }

b) x(2x - 1) + 6 = 4(x + 1)

2x² - x + 6 = 4x + 4

2x² - x - 4x + 6 - 4 = 0

2x² - 5x + 2 = 0

Δ = b² - 4ac

Δ = (-5)² - 4(2)(2)

Δ = 25 - 16

Δ = 9

x = - b ± √Δ / 2a

x = 5 ± 3 / 2(2)

x' = 5 + 3 / 4

x' = 8/4

x' = 2

x'' = 5 - 3/4

x'' = 2/4

x'' = 1/2

S = { 1/2, 2 }

c) (x - 1)*(x - 2) = 6

x² - 2x - x + 2 = 6

x² - 2x - x + 2 - 6 =0

x² - 3x - 4 = 0

Δ = b² - 4ac

Δ = (-3)² - 4(1)(-4)

Δ = 9 + 16

Δ = 25

x = - b ± √Δ / 2a

x = 3 ± 5 / 2(1)

x' = 3 + 5 / 2

x' = 8/2

x' = 4

x'' = 3 - 5 / 2

x'' = - 2/2

x'' = - 1

S = { - 1, 4 }

d) (2x - 3)*(x - 8) = 34

2x² - 16x - 3x + 24 = 34

2x² - 16x - 3x + 24 - 34 = 0

2x² - 19x - 10 = 0

Δ = b² - 4ac

Δ = (-19)² - 4(2)(-10)

Δ = 361 + 80

Δ = 441

x = - b ± √Δ / 2a

x = 19 ± 21 / 2(2)

x' = 19 + 21 / 4

x' = 40/4

x' = 10

x'' = 19 - 21 / 4

x'' = - 2/4

x'' = - 1/2

S = { - 1/2, 10 }