Question

50 2x4+3x3+16x+24=0
24x4+16x3-3x-2=0
решите
50 )​

Answer 1

1) 2x⁴ + 3x³ + 16x + 24 = 0

(2x⁴ + 16x) + (3x³ + 24) = 0

2x(x³ + 8) + 3(x² + 8) = 0

(x³ + 8)(2x + 3) = 0

или    x³ + 8 = 0   и тогда   x³ = - 8     x₁ = - 2

или    2x + 3 = 0   и тогда  2x = - 3     x₂ = - 1,5

ответ : - 2 ; - 1,5

2) 24x⁴ + 16x³ - 3x - 2 = 0

(24x⁴ + 16x³) - (3x + 2) = 0

8x³(3x + 2) - (3x + 2) = 0

(3x + 2)(8x³ - 1) = 0

3x + 2 = 0     3x = - 2     x₁ = - 2/3

8x³ - 1 = 0     8x³ = 1      x³ = 1/8     x₂ = 1/2

ответ : - 2/3 ; 1/2

Answer 2

Объяснение:

1)

${x}^{3} (2x + 3) + 8(2x + 3) = 0 \\ ( {x}^{3} + 8)(2x + 3) = 0 \\ x_{1} = \sqrt[3]{ - 8} = - 2 \\ x_{2} = - \frac{3}{2}$

2)

$8 {x}^{3} (3x + 2) - (3x + 2) = 0 \\ (8 {x}^{3} - 1)(3x + 2) = 0 \\ x_{1} = \sqrt[3]{ \frac{1}{8} } = \frac{1}{2} \\ x_{2} = - \frac{2}{3}$