Let be the cubic you need to find.

You know you have and .

Note that which gives you your .

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- Sep 3rd 2009, 11:44 PM #1

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## (αβ)(αγ)(βγ) = α²βγ+αβ²γ+αβγ² = [{α}/{αβγ}] + [{β}/{αβγ}] + [{γ}/{αβγ}]; No?

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Given that , , are the roots of the equation find the cubic equation whose roots are

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; ;

Since

the cubic equation is

Well, it turns out that the sum of roots in pairs should have been , not ; and in checking, I'm hell sure that

- Sep 3rd 2009, 11:59 PM #2

- Sep 4th 2009, 12:23 AM #3

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- Sep 4th 2009, 01:02 AM #4

- Sep 4th 2009, 09:59 PM #5