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Are the elementary symmetric polynomials "unique"?

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#polynomials #galois-theory #symmetric-polynomials
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Factoring $(a+b)(a+c)(b+c)=(a+b+c)(ab+bc+ca)-abc$

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#polynomials #factoring #symmetric-polynomials
609
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Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ?

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#polynomials #systems-of-equations #symmetric-polynomials
870
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Using Polya's Theorem to check positivity of a multivariate polynomial

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#polynomials #symmetric-polynomials #simplex
867
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Symmetric polynomial and vieta's formulas

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#symmetric-polynomials
166
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Writing $x^2+y^2+z^2$ as a polynomial combination of $xyz$, $x+y+z$, and $\frac1x+\frac1y+\frac1z$

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#algebra-precalculus #polynomials #symmetric-polynomials
1.1k
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If $x+\frac1x=5$ find $x^5+\frac1{x^5}\,$ [recurrence for power sums]

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#algebra-precalculus #analysis #polynomials #recurrence-relations #symmetric-polynomials
191
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Uniqueness of a solution of the system of equations

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#systems-of-equations #symmetric-polynomials
147
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How to solve the following system of equations.

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#systems-of-equations #symmetric-polynomials
78
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Have I done something wrong in solving the following pair of equations?

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#systems-of-equations #symmetric-polynomials
223
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How to solve the following pair of non-linear equations

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#systems-of-equations #symmetric-polynomials
183
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Identity with symmetric rational functions

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#symmetric-groups #symmetric-polynomials #symmetric-functions
136
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Express the power sum $\sum^{n}_{k=1}\alpha_{k}^n$ in terms of the coefficients of the polynomial $x^n+bx+c$.

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#polynomials #roots #symmetric-polynomials #symmetric-functions
544
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Derivative of the elementary symmetric functions

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#eigenvalues-eigenvectors #symmetric-polynomials #symmetric-matrices #symmetric-functions
103
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What will be $-(x_2-x_3)(x_3-x_1)(x_1-x_2)$?

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#roots #symmetric-polynomials

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