Question

Найдите корни уравнения
40+16х-2/х^2-5/х^3=0

Answer 1

40+16x-2/x²-5/x³=0  |×x³                        ОДЗ: х²≠0   х³≠0   х≠0
40x³+16x⁴-2x-5=0
16x⁴+40x³-2x-5=0
x₁=0,5
16x⁴+40x³-2x-5   |_x-0,5_
16x⁴-8x³                | 16x³+48x²+22x+10
------------
            48x³-2x
            48x³-24x²
            ------------
                     22x²-2x
                     22x²-12x
                     ------------
                               10x-5
                               10x-5
                                -------
                                        0
16x³+48x²+22x+10=0
x₂=-2,5
16x³+48x²+22x+10  |_x+2,5_
16x³+40x²                  | 16x²+8x+2
------------
              8x²+22x
              8x²+20x
             ------------
                        2x+10
                        2x+10
                        --------
                                  0
16x²+8x+2=0    |÷2
8x²+4x+1=0     D=-16  ⇒  Уравнение не имеет действительных корней.
Ответ: х₁=0,5     х₂=-2,5.