Question

z^4-12z^2-64=0 ecuatie bipatratica

Answer 1

${z}^{4} - 12 {z}^{2} - 64 = 0$

${z}^{2} = t$

${t}^{2} - 12t - 64 = 0$

${t}^{2} + 4t - 16t - 64 = 0$

$t(t + 4) - 16(t + 4) = 0$

$(t - 16)(t + 4) = 0$

$t - 16 = 0 = > t = 16$

$t + 4 = 0 = > t = - 4$

${z}^{2} = 16 = > z = \pm \sqrt{16} = \pm4$

${z}^{2} = - 4 = > z = \pm \sqrt{ - 4} = \pm i \sqrt{4} = \pm2i$