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Feb 16th, 2022
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  1. k_a = float(input("Введите A: "))
  2. k_b = float(input("Введите B: "))
  3. k_c = float(input("Введите C: "))
  4. k_d = float(input("Введите D: "))
  5. a = k_b / k_a
  6. b = k_c / k_a
  7. c = k_d / k_a
  8. q = (a**2 - 3 * b) / 9
  9. r = (2 * a**3 - 9 * a * b + 27 * c) / 54
  10. s = q**3 - r**2
  11. if s > 0:
  12. from math import acos, cos, sqrt, pi
  13. f = (1 / 3) * acos(r / sqrt(q**3))
  14. x1 = -2 * sqrt(q) * cos(f) - (a / 3)
  15. x2 = -2 * sqrt(q) * cos(f + (2 / 3) * pi) - (a / 3)
  16. x3 = -2 * sqrt(q) * cos(f - (2 / 3) * pi) - (a / 3)
  17. print("Q = ", q)
  18. print("R = ", r)
  19. print("S = ", s)
  20. print("fi = ", f)
  21. print("x1 = ", x1)
  22. print("x2 = ", x2)
  23. print("x3 = ", x3)
  24. elif s < 0:
  25. if q > 0:
  26. from cmath import acosh, cosh, sinh, sqrt
  27. f = (1 / 3) * acosh((abs(r)) / (sqrt(q**3)))
  28. if r > 0:
  29. x1 = -2 * sqrt(q) * cosh(f) - (a / 3)
  30. x2 = sqrt(q) * cosh(f) - (a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
  31. x3 = sqrt(q) * cosh(f) + (a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
  32. print("Q = ", q)
  33. print("R = ", r)
  34. print("S = ", s)
  35. print("fi = ", f)
  36. print("x1 = ", x1)
  37. print("x2 = ", x2)
  38. print("x3 = ", x3)
  39. elif r == 0:
  40. x1 = -a / 3
  41. x2 = (-a / 3) - 1j * sqrt(3) * sqrt(q) * sinh(f)
  42. x3 = (-a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
  43. print("Q = ", q)
  44. print("R = ", r)
  45. print("S = ", s)
  46. print("fi = ", f)
  47. print("x1 = ", x1)
  48. print("x2 = ", x2)
  49. print("x3 = ", x3)
  50. else:
  51. x1 = 2 * sqrt(q) * cosh(f) - a / 3
  52. x2 = -1 * sqrt(q) * cosh(f) - a / 3 + 1j * sqrt(3) * sqrt(q) * sinh(f)
  53. x3 = -1 * sqrt(q) * cosh(f) - a / 3 - 1j * sqrt(3) * sqrt(q) * sinh(f)
  54. print("Q = ", q)
  55. print("R = ", r)
  56. print("S = ", s)
  57. print("fi = ", f)
  58. print("x1 = ", x1)
  59. print("x2 = ", x2)
  60. print("x3 = ", x3)
  61. elif q < 0:
  62. from cmath import asinh, cosh, sinh, sqrt
  63. f = (1 / 3) * asinh(abs(r) / sqrt(q**3))
  64. if r > 0:
  65. x1 = -2 * sqrt(abs(q)) * sinh(f) - a / 3
  66. x2 = sqrt(abs(q)) * sinh(f) - a / 3 + 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
  67. x3 = sqrt(abs(q)) * sinh(f) - a / 3 - 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
  68. print("Q = ", q)
  69. print("R = ", r)
  70. print("S = ", s)
  71. print("fi = ", f)
  72. print("x1 = ", x1)
  73. print("x2 = ", x2)
  74. print("x3 = ", x3)
  75. elif r == 0:
  76. x1 = -a / 3
  77. x2 = -a / 3 + 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
  78. x3 = -a / 3 - 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
  79. print("Q = ", q)
  80. print("R = ", r)
  81. print("S = ", s)
  82. print("fi = ", f)
  83. print("x1 = ", x1)
  84. print("x2 = ", x2)
  85. print("x3 = ", x3)
  86. else:
  87. x1 = 2 * sqrt(abs(q)) * sinh(f) - a / 3
  88. x2 = -1 * sqrt(abs(q)) * sinh(f) - a / 3 + 1j * sqrt(3) * cosh(f)
  89. x3 = -1 * sqrt(abs(q)) * sinh(f) + a / 3 + 1j * sqrt(3) * cosh(f)
  90. print("Q: = ", q)
  91. print("R = ", r)
  92. print("S = ", s)
  93. print("fi = ", f)
  94. print("x1 = ", x1)
  95. print("x2 = ", x2)
  96. print("x3 = ", x3)
  97. else:
  98. from cmath import sqrt
  99. x1 = -((c - (a * 3) / 27))**(1 / 3) - a / 3
  100. x2 = (-a + x1) / 2 + 1j / 2 * sqrt(abs((a - 3 * x1) * (a + x1) - 4 * b))
  101. x3 = x2 = (-a + x1) / 2 - 1j / 2 * sqrt(abs((a - 3 * x1) * (a + x1) - 4 * b))
  102. print("Q = ", q)
  103. print("R = ", r)
  104. print("S = ", s)
  105. print("fi = ", f)
  106. print("x1 = ", x1)
  107. print("x2 = ", x2)
  108. print("x3 = ", x3)
  109. else:
  110. x1 = -2 * (r)**(1 / 3) - a / 3
  111. x2 = (r)**(1 / 3) - a / 3
  112. print("Q = ", q)
  113. print("R = ", r)
  114. print("S = ", s)
  115. print("fi = ", f)
  116. print("x1 = ", x1)
  117. print("x2 = ", x2)
  118.  
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