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Is it possible to find these numbers without converting them into cubic equation?

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#systems-of-equations #symmetric-polynomials
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Symmetric powers of $\mathbb{P}^1$

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#algebraic-geometry #symmetric-polynomials #invariant-theory
242
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Symmetric polynomials in quotient of polynomial rings.

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#abstract-algebra #polynomials #symmetric-polynomials
96
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Ideal in the ring of symetric polynomials

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#polynomials #ring-theory #symmetric-polynomials
1.1k
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Schur polynomials form a basis for the space of symmetric polynomials

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#polynomials #symmetric-polynomials
8.3k
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Find $S = \frac{a}{b+c}+\frac{b}{c+a} + \frac{c}{a+b}$ if values of $a+b+c$ and $\frac1{a+b}+\frac1{b+c}+\frac1{a+c}$ are given

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#algebra-precalculus #contest-math #symmetric-polynomials
62
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Find all solutions to sys. of equation

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#systems-of-equations #cubics #symmetric-polynomials
81
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Evaluate the following Determinant of $12$th degree polynomial

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#linear-algebra #matrices #determinant #symmetric-polynomials
38
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Solving a series of system equations

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#systems-of-equations #symmetric-polynomials
85
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Representation of polar forms corresponding to b-splines

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#symmetric-polynomials #spline
163
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show that $x+y+z\ge 2$

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#inequality #polynomials #optimization #symmetric-polynomials #a.m.-g.m.-inequality
82
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How prove this inequality $\sum_{cyc}\frac{a^4}{a^2+2b^4}\ge 1$

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#inequality #polynomials #fractions #symmetric-polynomials #cauchy-schwarz-inequality
532
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Proving $a^{-2}bcd+b^{-2}cda+c^{-2}dab+d^{-2}abc\geqslant a+b+c+d$

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#inequality #symmetric-polynomials #a.m.-g.m.-inequality #muirhead-inequality
117
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How to express sum of three roots of a polynomial?

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#abstract-algebra #algebra-precalculus #symmetric-polynomials
767
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Schur function principal specialisation

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#combinatorics #representation-theory #symmetric-groups #symmetric-polynomials #young-tableaux

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