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Prove $(x+y+z)^8\ge 3^7(x^2+y^2+z^2)x^2y^2z^2$

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#inequality #substitution #symmetric-polynomials #a.m.-g.m.-inequality #uvw
115
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Quadratic equation, find $1/x_1^3+1/x_2^3$

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#algebra-precalculus #polynomials #roots #quadratics #symmetric-polynomials
87
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Find a polynomial with roots which are functions of roots of an irreducible polynomial

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#linear-algebra #polynomials #field-theory #roots #symmetric-polynomials
156
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Inequalities of expressions completely symmetric in their variables

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#inequality #symmetric-polynomials #symmetric-functions
277
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Proving the inequality $(a^2-ab+b^2)(c^2-ac+a^2)(b^2-bc+c^2) \le 12$.

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#algebra-precalculus #inequality #symmetric-polynomials #a.m.-g.m.-inequality
36
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How to solve the following equation depending on $a$,$b$,$c$?

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#systems-of-equations #symmetric-polynomials
366
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Inequality trouble: $(a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2) \geq (ab+bc+ca)^3$

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#inequality #contest-math #substitution #symmetric-polynomials #uvw
296
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Dimension of Homogenous Symmetric Polynomials with $(k,r)$-Clustering Property

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#representation-theory #symmetric-polynomials
400
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Representation of symmetric function

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#multivariable-calculus #symmetric-polynomials #symmetric-functions
988
Views

Express power sums in terms of elementary symmetric functions

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#abstract-algebra #polynomials #symmetric-polynomials #symmetric-functions
84
Views

How can I prove sum of the squares of the roots of $x^3+ax^2+bx+c$ is equal to $a^2-2b$?

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#algebra-precalculus #polynomials #roots #cubics #symmetric-polynomials
812
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Proving the generating functions version of Newton's identities

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#abstract-algebra #polynomials #generating-functions #symmetric-polynomials #symmetric-functions
833
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Simultaneous equation $x^2 +y=10050$ and $y^2 + x= 2600$ solution

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#systems-of-equations #diophantine-equations #symmetric-polynomials
334
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Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.

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#elementary-number-theory #square-numbers #symmetric-polynomials
323
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Prove the identity between formal power series in t

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#abstract-algebra #power-series #exponential-function #generating-functions #symmetric-polynomials

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