I have a problem but i don't know what method i should use to solve it.

If x^3 – 2x^2 + 3x = 6 prove x=2

Apologies for the poor format of the equation.

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- August 26th 2009, 07:06 AMMaths Stigproblem
I have a problem but i don't know what method i should use to solve it.

If x^3 – 2x^2 + 3x = 6 prove x=2

Apologies for the poor format of the equation. - August 26th 2009, 07:32 AMLiwuinan
subtract 6 from both sides and factorize the left side:

Assuming x should be a real number, this can equal to zero if and only if at least one of the brackets is zero and this happens if and only if x=2 (first bracket is never zero). In complex numbers there would be also other solutions, not only x=2. - August 26th 2009, 07:34 AMDefunkt
We will solve this using the fact that

If we assume (where are the real numbers), then the solution for equation would be either the solution for or . Obviously, is a solution, and there are no other solutions for in , thus

If you want to solve this equation over (the complex numbers), then , are also solutions, but I don't think this is the case.