Question

Решить биквадратное уравнение:

x^4-12x^2-64=0

Answer 1

.....................

Answer 2

$\displaystyle \tt {x}^{4} - 12 {x}^{2} - 64 = 0$

Пусть $\displaystyle \tt x^2=y$, тогда:

$\displaystyle \tt {y}^{2} - 12 {y}^{2} - 64 = 0 \\ D = {( - 12)}^{2} - 4 \cdot 1 \cdot ( - 64) = 144 + 256 = 400 \\ \sqrt{D} = \sqrt{400} = 20 \\ y_1 = \frac{12 + 20}{2} = \frac{32}{2} = 16 \\ y_2 = \frac{12 - 20}{2} = \frac{ - 8}{2} = - 4$

$\displaystyle \tt {x}^{2} = 16 \\ x = \sqrt{16} \\ x_1 = 4 \\ x = - \sqrt{16} \\ x_2= - 4$

$\displaystyle \tt x^2=-4$ - нет корней

Ответ: $\displaystyle \tt x_1=4; \: x_2=-4$