stickman lore Official š | 2048 / 0 to ????? Inf
Cbrt(x) of a complex numbersDEEDEDo some expansion (a+bi)Ā³=aĀ³+3aĀ²bi-3abĀ²-bĀ³i=(aĀ³-3abĀ²)+(3aĀ²b-bĀ³)i(aĀ³-3abĀ²)=c, (3aĀ²b-bĀ³)=d(aĀ³-3abĀ²)=cLets act c as a constanta(aĀ²-3bĀ²)=c(aĀ²-3bĀ²)=c/a(-3bĀ²)=c/a - aĀ²(bĀ²)=(aĀ² - c/a)/3(b)=sqrt((aĀ² - c/a)/3)(3aĀ²sqrt((aĀ² - c/a)/3)-sqrt((aĀ² - c/a)/3)Ā³)=d(3aĀ²sqrt((aĀ² - c/a)/3)-sqrt((aĀ² - c/a)/3)Ā³)=d[(aĀ² - c/a)/3] * [(8aĀ² + c/a)Ā² / 9] = dĀ²(aĀ²/3 - c/a) * (aĀ²/3 - c/a - 3aĀ²)Ā² = dĀ²(aĀ²/3 - c/a) * (aĀ²/3 - c/a - 3aĀ²)Ā² = dĀ²64aā¶/27 - 16aĀ³c/3 - 5cĀ² - cĀ³/aĀ³ = dĀ²64aā¹/27 - 16aā¶c/3 - 5cĀ²aĀ³ - cĀ³ = dĀ²aĀ³t=aĀ³64tĀ³/27 - 16tĀ²c/3 - 5cĀ²t - t = dĀ²t64tĀ³/27 - 16tĀ²c/3 - (5cĀ²-dĀ²)t - t =064tĀ³/27 - 16tĀ²c/3 - (5cĀ²-dĀ²-1)t=0(64/27)xĀ³+(-9cĀ²+dĀ²+1)x+1/4(-23cĀ³+3cdĀ²+3c)t=x+3c/4(64/27)xĀ³+(-9cĀ²+dĀ²+1)x+1/4(-23cĀ³+3cdĀ²+3c)x=Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)), (omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))), (omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))t=((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4, (omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4, (omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4a=cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4), cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4), cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)(b)=sqrt(((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4))Ā² - c/(cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)))/3), sqrt(((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3), sqrt(((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3)------------------------------Cbrt((c,d))=((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)),(sqrt(((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4))Ā² - c/(cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)))/3))), ((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)),(sqrt(((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3))), ((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)),(sqrt(((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3)))
2 months ago | [YT] | 0
stickman lore Official š | 2048 / 0 to ????? Inf
Cbrt(x) of a complex numbers
DEEDE
Do some expansion
(a+bi)Ā³=aĀ³+3aĀ²bi-3abĀ²-bĀ³i=(aĀ³-3abĀ²)+(3aĀ²b-bĀ³)i
(aĀ³-3abĀ²)=c, (3aĀ²b-bĀ³)=d
(aĀ³-3abĀ²)=c
Lets act c as a constant
a(aĀ²-3bĀ²)=c
(aĀ²-3bĀ²)=c/a
(-3bĀ²)=c/a - aĀ²
(bĀ²)=(aĀ² - c/a)/3
(b)=sqrt((aĀ² - c/a)/3)
(3aĀ²sqrt((aĀ² - c/a)/3)-sqrt((aĀ² - c/a)/3)Ā³)=d
(3aĀ²sqrt((aĀ² - c/a)/3)-sqrt((aĀ² - c/a)/3)Ā³)=d
[(aĀ² - c/a)/3] * [(8aĀ² + c/a)Ā² / 9] = dĀ²
(aĀ²/3 - c/a) * (aĀ²/3 - c/a - 3aĀ²)Ā² = dĀ²
(aĀ²/3 - c/a) * (aĀ²/3 - c/a - 3aĀ²)Ā² = dĀ²
64aā¶/27 - 16aĀ³c/3 - 5cĀ² - cĀ³/aĀ³ = dĀ²
64aā¹/27 - 16aā¶c/3 - 5cĀ²aĀ³ - cĀ³ = dĀ²aĀ³
t=aĀ³
64tĀ³/27 - 16tĀ²c/3 - 5cĀ²t - t = dĀ²t
64tĀ³/27 - 16tĀ²c/3 - (5cĀ²-dĀ²)t - t =0
64tĀ³/27 - 16tĀ²c/3 - (5cĀ²-dĀ²-1)t=0
(64/27)xĀ³+(-9cĀ²+dĀ²+1)x+1/4(-23cĀ³+3cdĀ²+3c)
t=x+3c/4
(64/27)xĀ³+(-9cĀ²+dĀ²+1)x+1/4(-23cĀ³+3cdĀ²+3c)
x=Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)), (omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))), (omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))
t=((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4, (omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4, (omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4
a=cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4), cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4), cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)
(b)=sqrt(((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4))Ā² - c/(cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)))/3), sqrt(((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3), sqrt(((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3)
------------------------------
Cbrt((c,d))=((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)),(sqrt(((cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4))Ā² - c/(cbrt(((Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³))))-3c/4)))/3))), ((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)),(sqrt(((cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaCbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3))), ((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)),(sqrt(((cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4))Ā² - c/(cbrt((omegaĀ²Cbrt((27/512)(23cĀ³-3cd-3c)+sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)) + omegaCbrt((27/512)(23cĀ³-3cd-3c)-sqrt(((27/512)(-23cĀ³+3cd+3c))Ā²+((9/64)(-9cĀ²+dĀ²+1))Ā³)))-3c/4)))/3)))
2 months ago | [YT] | 0