Solving A Nice Cubic Equation | Math Olympiads

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There's another to find the complex solutions:
9x³ + 3x² + 3x + 1 = 0

Factor by grouping (3x+1)

3x²(3x+1) +1(3x+1) = 0

3x+1 is a common factor, so we can take it out.

(3x+1)(3x²+1) = 0

First one is 3x+1=0
3x = -1
x = -1/3

The other one is 3x²+1=0
x² = -1/3

Square root both sides (Don't forget plus or minus sign and rationalize the fraction).

x = ±√(-1/3)
x = ±i√(1/3)
x = ±i1/√3

JeremyLionell
Автор

Not every x³ forme can be easly or even transformed to a perfect cube

sedx
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Orma third method sum of two.cibes gives (2x)
^3 + (×+1)^3 = (2× + x +1)((2x)^2 -2x(x+1) + (×+1)^2)= 0 and then use quadratic formula tomsolve the quadratic term..

leif