Question

Równania wielomianowe. Rozwiąż równania

A)x^{4} - x^{2} - 12 = 0

B) x^{6} - 26x^{3} - 27 = 0

Liczę na szybkie rozwiązanie dam naj, pozdrawiam :)

Answer 1

A)

x^{4} - x^{2} - 12 = 0

x^2 = t   i t > 0

t^2 - t - 12 = 0

Δ = 1 + 48 = 49

√Δ = 7

t1 = (1 - 7)/2 = -6/2 = -3  < 0

t2 = (1 + 7)/2 = 8/2 = 4 > 0

 

x^2 = t

x^2 = 4

x = 2   lub   x = -2

 

B)

 x^{6} - 26x^{3} - 27 = 0

x^3 = t

t^2 - 26t - 27 = 0

Δ = 676 + 108 = 784

√Δ = 28

t1 = (26 - 28)/2 = -2/2 = -1

t2 = (26 + 28)/2 = 54/2 = 27

 

x^3 = t

x^3 = -1            lub       x^3 = 27

x = -1                lub         x = 3