Question

6 Resolva, em R, as equações a seguir: a) (-x2 + 1) - (x2 – 3x + 2) = 0 b) (x – 1) · (x - 2) = (x - 1) · (2x + 3) c) (x + 5)2 = (2x - 3)2 d) x3 + 10x2 + 21x = 0 e) x4 – 5x2 + 4 = 0​

Answer 1

Vamos là.

a)

(-x^2 + 1) - (x^2 – 3x + 2) = 0

-2x^2 + 3x - 1 = 0

2x^2 - 3x + 1 = 0

a = 2, b = -3 , c = 1

delta

d = 9 + 8 = 1

x1 = (3 + 1)/4 = 1

x2 = (3 - 1)/4 = 1/2

b)

(x – 1) * (x - 2) = (x - 1) * (2x + 3)

x^2 - 3x + 2 = 2x^2 + x - 3

x^2 + 4x - 5 = 0

delta

d = 36

x1 = (-4 + 6)/2 = 1

x2 = (-4 - 6=/2 = -5

c)

(x + 5)^2 = (2x - 3)^2

x^2 + 10x + 25 = 4x^2 - 12x + 9

3x^2 - 22x - 16 = 0

delta

d = 22^2 + 12*16 = 676

x1 = (22 + 26)/6 = 8

x2 = (22 - 26)/6 = -2/3

d)

x^3 + 10x^2 + 21x = 0

x*(x^2 + 10x + 21) = 0

delta

d = 10^2 - 4*21 = 16

x1 = (-10 + 4)/2 = -3

x2 = (-10 - 4)/2 = -7

x3 = 0

e)

x^4 – 5x^2 + 4 = 0​

delta

d = 25 - 16 = 9

x^2 = (5 + 3)/2 = 4

x^2 = (5 - 3)/2 = 1

x1 = 2, x2 = -2, x3 = 1, x4 = -1