Question

dau coroană
Va rog frumos

​

Answer 1

Răspuns:

Explicație pas cu pas:

$f = X^{4} - 4 = (X^{2} - 2)(X^{2} + 2) = (X - \sqrt{2} )(X + \sqrt{2} )(X - i\sqrt{2})(X + i\sqrt{2})$

$\implies x_{1;2} = \pm \sqrt{2} ; \ x_{3;4} = \pm i\sqrt{2}$

$g = X^{3} -4X + 3 = X^{3} - X^{2} + X^{2} -X -3X + 3 = (X - 1)(X^{2} + X - 3)$

$x^{2} + x - 3 = 0$

$\Delta = 1 + 12 = 13 \implies x_{2;3} = \dfrac{-1 \pm \sqrt{13} }{2}$

$x_{1} = 1 ; \ x_{2;3} = \dfrac{-1 \pm \sqrt{13} }{2}$