Question

Решить уравнение очень х⁴+77х²-36=0

Answer 1

$-\frac{2}{3};\frac{2}{3}$

Объяснение:

$9x^4+77x^2-36=0\\3AMEHA: x^2 = t, t \ge 0\\9t^2+77t-36=0\\D=77^2-4*9*(-36)=77^2+36^2=5929+1296=85^2\\t_1=\frac{-77+\sqrt{85^2}}{2*9}=\frac{-77+85}{18}=\frac{8}{18}=\frac{4}{9}\\t_2=\frac{-77-\sqrt{85^2}}{2*9}=\frac{-77-85}{18}=\frac{-162}{18}=-\frac{18*9}{18}=-9$

$\left[\begin{gathered}t=\frac{4}{9},\\t=-9;\end{gathered}\right.\\\left[\begin{gathered}x^2=\frac{4}{9},\\x^2=-9;\end{gathered}\right.\\x^2=\frac{4}{9}\\x^2=\pm\frac{2}{3}$