I need to find x and y in terms of t and s.

Help?

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- Oct 17th 2012, 06:35 AMpatpatpats = x^2 + y^2, t = 2xy
I need to find x and y in terms of t and s.

Help? - Oct 17th 2012, 06:56 AMemakarovRe: s = x^2 + y^2, t = 2xy
We have , or . By Vieta's formulas, x and y are the roots of the quadratic equation .

- Oct 17th 2012, 07:13 AMpatpatpatRe: s = x^2 + y^2, t = 2xy
Excuse the ignorance, but I'm unfamiliar with Vieta's Formulas. I understand that - didn't realise this forum had tex in bb, that's pretty cool - but how do I go about the next step? I'm still at a loss at how to attain my final two x and y equations that I need.

- Oct 17th 2012, 07:27 AMemakarovRe: s = x^2 + y^2, t = 2xy
Vieta's formulas for quadratic equations are easy to derive. If an equation has roots x and y, then by the polynomial remainder theorem (the link has a short proof). Expanding the right-hand side and equating the coefficients of and z in both sides, we get b = -(x + y) and c = xy. So, x and y are the roots of . You can express the coefficients of this equation through s and t.

Once you have a quadratic equation with roots x and y, they can be expressed through s and t using the quadratic formula.