Tenglamani yeching

[Meritocrat]

Tenglamani yeching (X ga nisbatan)

1) X^3 + PX + Q = 0

va shundan foydalanib quyidagi tenglamani yeching

2) AX^3 + BX^2 + CX + D = 0

Matematikaga qiziquvshilar uchun!

[Kastryulka]

Tenglamani yeching (X ga nisbatan)

1) X^3 + PX + Q = 0

va shundan foydalanib quyidagi tenglamani yeching

2) AX^3 + BX^2 + CX + D = 0

Matematikaga qiziquvshilar uchun!

matriza shaklida yechish kerakmi?

ax^3 + bx^2 + cx + d = 0
Devide by 'a', get
x^3 + ex^2 + fx + g = 0
Substitute u = x + e/3, get
u^3 + pu + q = 0
(where p = f - (e^2)/3 and q = 2(e^3)/27 - ef/3 + g)

u^3 - 3pu - 2q = 0
(where p = (e^2)/9 - f/3 and q = ef/6 - (e^3)/27 - g/2)
Find (r, s) such that
r + s = 2q and rs = p^3
(r = q + (q^2 - p^3)^(1/2), and s = q - (q^2 - p^3)^(1/2))
Then,
u = r^(1/3) + s^(1/3) and
x = u - e/3

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