Question

Obtenha a forma reduzida de cada equaçao e determine suas raizes:
a)x2-4x=5
b) (x+1).(x-2)=-7x-10
c)3x.(x-2)=2.(x+3/2)

Answer 1

b)(x+1).(x-2)=7x-10
x2-2x+1x-2=7x-10
x2-2x+1x-7x-2+10=0
x2-9x+1x+8=0
x2-8x+8=0

Answer 2

x² - 4x = 5
x² - 4x - 5 = 0

a = 1
b = - 4
c = - 5

Δ = b² - 4ac
Δ = (-4)² - 4.(1).(-5)
Δ = 16 + 20
Δ = 36

x = - b +/- √Δ
           2a

x = 4 + 6 = 10/2 = 5
        2

x = 4 - 6 = - 2/2 = - 1
         2
___________________________
b)
(x + 1).(x - 2) = - 7x - 10

x² - 2x + x - 2 = - 7x - 10
x² - x - 2 + 7x + 10 = 0
x² + 6x + 8 = 0

a = 1; b = 6; c = 8

Δ = b² - 4ac
Δ = 6² - 4.1.8
Δ = 36- 32
Δ = 4

x = - b +/- √Δ
           2a

x = - 6 + 2 = - 4/2 = - 2
          2
x = - 6 - 2 = - 8/2 = - 4
          2
____________________________
c)
3x(x - 2) = 2.(x + 3)
                  (      2)

3x² - 6x = 2x + 6
                       2

3x² - 6x = 2x + 3
3x² - 6x - 2x - 3 = 0
3x² - 8x - 3 = 0

a = 3; b = - 8; c = - 3

Δ = b² - 4ac
Δ = (-8)² - 4.3.(-3)
Δ = 64 + 36
Δ = 100

x = - b +/-√Δ
          2a

x = 8 + 10 = 18/6 = 3
          6
x = 8 - 10 = - 2 (:2) = - 1
         6         6 (:2)      3