Question

Розв’язати біквадратне рівняння:

x4 + 5x2 + 4 = 0

Answer 1

${x}^{4} + 5 {x}^{2} + 4 = 0 \\ {x}^{2} = ξ \\ {ξ}^{2} + 5 ξ + 4 = 0 \\ D = {b}^{2} - 4ac = {5}^{2} - 4 \times 1 \times 4 = 9 \\ξ_{1} = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 5 - \sqrt{9} }{2 \times 1 } = \frac{ - 8}{2} = - 4 \\ ξ_{2} = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 5 + \sqrt{9} }{2 \times 1} = - 1 \\ \\ ξ_{1} = x_{1,2} {}^{2} \\ ξ_{2} = x_{3,4} {}^{2} \\ \\ x_{1,2} = ±\sqrt{ - 1} \\ x_{3,4} = ± \sqrt{ - 4} \\ \\ x_{1,2} = ±i \\ x_{3,4} = ± 2i$