Question

1) Resolva as equações biquadradas.

a)(x2 - 1)2 + (x2 - 3)2 =10

b) (x2 + 3)2 = 19.(x2 + 3) - 84

c)(x2 + 1)2 + (x2 - 1)2 = 4x?

d) (2x - 1).(2x + x2 + 2x + 1) = 26​

Answer 1

Resposta:

a) (x² - 1)² + (x² - 3)² = 10

x⁴ - 2x² + 1 + x⁴ - 6x² + 9 = 10

2x⁴ - 8x² = 0

x⁴ - 4x² = 0

x² * (x²  - 4) = 0

x1 = 0

x2 = 2

x3 = -2

b) (x² + 3)² = 19*(x² + 3) - 84

x⁴ + 6x² + 9 = 19x² + 57 - 84

x⁴ - 13x² + 36 = 0

y² - 13y + 36 = 0

delta

d = 169 - 144 = 25

y1 = (13 + 5)/2 = 9

y2 = (13 - 5)/2 = 4

x1 = -3, x2 = 3

x3 = -2, x4 = 2

c)(x² + 1)² + (x² - 1)² = 4x

d) (2x - 1)*(2x³ + x² + 2x + 1) = 26​ (esta 2x³)

4x⁴ + 2x³ + 4x² + 2x - 2x³ - x² - 2x - 1 = 26

4x⁴ + 3x² - 27 = 0

(2x - 3) (2x + 3) (x² + 3) = 0

2x1 - 3 = 0

x1 = 3/2

2x2 + 3 = 0

x2 = -3/2