1. ## equation

Hey guys, I have some math homework...
The last equation I can't solve is that:

(x^2+x+1)^2(x^2-x+1)=3

Thanks!

2. Originally Posted by dgolverk
Hey guys, I have some math homework...
The last equation I can't solve is that:

(x^2+x+1)^2(x^2-x+1)=3

Thanks!
$x^6+x^5+2x^4+x^3+2x^2+x-2=0$

Using the rational roots test the possible rational zeros are x = +/- 1, +/- 2. The only rational solution is x = -1. Using synthetic division on the zero x = -1 gives:
$x^5+2x^3-x^2+3x-2=0$
which does have a real solution near x = 0.611 (so the other 4 are complex), but being a 5th degree polynomial equation I don't have a way to generally solve it exactly.

-Dan

3. Isn't there other way?
It's somehow supposed to be related to quadratic equations or something.

4. Originally Posted by dgolverk
Isn't there other way?
It's somehow supposed to be related to quadratic equations or something.
There may be a trick involved. I noted when I looked at the problem that each factor is related to the factorization of the sum and difference of two cubes:
$x^3 - 1 = (x-1)(x^2+x+1)$
and
$x^3+1=(x+1)(x^2-x+1)$

However, I can't think of a way to use this information. That 3 on the RHS spoils things pretty badly for me. Sorry!

-Dan

5. I see...thanks anyway
someone else can help?