Well you could form a polynomial with roots alpha^2, beta^2, gamma^2, delta^2. And then finding the sum of roots (-b/a) of that polymomial
For roots of a polynomial stuff, do you have to remember like alpha^2 + beta^2 + gamma^2 + delta^2 and what this is equivalent to? I know alpha^2 + beta^2 = (alpha+beta)^2 - 2alpha*beta but do we have to remember the hard ones like shown above? If we do is there a way to derive them?
2016 HSC (Accelerated)
// 2 Unit Maths // Studies of Religion 1 //
2017 HSC
// Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //
Well you could form a polynomial with roots alpha^2, beta^2, gamma^2, delta^2. And then finding the sum of roots (-b/a) of that polymomial
0.o
https://en.wikipedia.org/wiki/Newton's_identities .
As background reading too, you may want to see:
- https://en.wikipedia.org/wiki/Symmetric_polynomial
- https://en.wikipedia.org/wiki/Elemen...ric_polynomial (and this part: https://en.wikipedia.org/wiki/Elemen...ic_polynomials (which was asked as a question by glittergal96 in a previous MX2 Advanced Level marathon here: HSC 2016 MX2 Marathon ADVANCED (archive))).
Is there any way to do all this stuff using pythagorus? I mean with all the a^2, b^2
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