Question

х4+4х3-2х2-4х+1=0
Розв'язати рівняння​

Answer 1

Ответ:

${x}^{4} + 4 {x}^{3} - 2 {x}^{2} - 4x + 1 = 0 \ {x}^{2} + 4x - 2 - frac{4}{x} + frac{1}{ {x}^{2} } = 0 \ ({x}^{2} - 2 + frac{1}{ {x}^{2} }) + 4(x - frac{1}{x} ) = 0 \ \ x - frac{1}{x} = y \ {y}^{2} + 4y = 0 \ y = 0 \ y = - 4 \ x - frac{1}{x} = 0 \ {x}^{2} - 1 = 0 \ x = + - 1 \ x - frac{1}{x} = - 4 \ {x }^{2} + 4x - 1 = 0 \ d = 20 \ x3.4 = = frac{ - 4 + - sqrt{20} }{2} = - 2 + - sqrt{5}$