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Polynomial Equation

Posted May 1st, 2009 by alpha
in

Within what limits of must 'a' lie so that the two of the roots of the equation $ (a-1)(x^2+x+1)^2=(a+1)(x^4+x^2+1) $ .

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QUESTION

On May 4th, 2009 alpha says:

Within "WHAT LIMITS" must 'a' lie so that the two of the roots of the equation $ (a-1)(x^2+x+1)^2=(a+1)(x^4+x^2+1) $ .

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answer

On May 2nd, 2009 Structure says:

$ (a-1)(x^2+x+1)^2=(a+1)(x^4+x^2+1) $

$$x^4+x^2+1=x^4+2x^2+1-x^2=(x^2+1)^2-x^2=(x^2+1+x)(x^2+1-x)=(x^2+x+1)(x^2-x+1)$$

So you have

$$(x^2+x+1)(x^2-ax+1)=0$$

question

On May 1st, 2009 Structure says:

I don't understand the question.Please be more explicit.

There are no more informations .

On May 3rd, 2009 alpha says:

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there is no question

On May 3rd, 2009 Structure says:

Your text has no question.
I have solved the equation for you

This is what given in the question.

On May 2nd, 2009 alpha says:

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My method

On May 1st, 2009 alpha says:

Let $ x^2+x $=b

$ (a-1)(x^2+x+1)^2=(a+1)(x^4+x^2+1) $
$ (a-1)(b+1)^2=(a+1)[(b^2-2x^3)+1] $ .
$ \frac{a-1}{a+1}=\frac{b^2-2x^3 }{(b+1)^2} $
I am familiar with the expression in LHS ..... can dividendo & componendo rule be used?
Am I going in the right direction?

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