а) 0,7 x^4 - x^3 = 00,7x^4 = x^30,7x = 1x = 1 / 0,7x = 10 / 7
б) 0,5x^3 - 72 = 00,5x^3 = 72x^3 = 72 / 0,5x^3 = 144x = ∛144x = 4
в) x^3 + 4x = 5x^2x^3 + 4x - 5x^2 = 0x(x^2 - 5x + 4) = 0x(x - 4)(x - 1) = 0x = 0, x = 4, x = 1
г) 3x^3 - x^2 + 18x - 6 = 0x^2(3x - 1) + 6(3x - 1) = 0(x^2 + 6)(3x - 1) = 0x^2 + 6 = 0x^2 = -6x = √(-6)x = ±√6i
Ответ:а) x ≈ 1,43б) x = 4в) x = 0, x = 4, x = 1г) x = ±√6i
а) 0,7 x^4 - x^3 = 0
0,7x^4 = x^3
0,7x = 1
x = 1 / 0,7
x = 10 / 7
б) 0,5x^3 - 72 = 0
0,5x^3 = 72
x^3 = 72 / 0,5
x^3 = 144
x = ∛144
x = 4
в) x^3 + 4x = 5x^2
x^3 + 4x - 5x^2 = 0
x(x^2 - 5x + 4) = 0
x(x - 4)(x - 1) = 0
x = 0, x = 4, x = 1
г) 3x^3 - x^2 + 18x - 6 = 0
x^2(3x - 1) + 6(3x - 1) = 0
(x^2 + 6)(3x - 1) = 0
x^2 + 6 = 0
x^2 = -6
x = √(-6)
x = ±√6i
Ответ:
а) x ≈ 1,43
б) x = 4
в) x = 0, x = 4, x = 1
г) x = ±√6i