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15
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Symmetric polynomial written in elementary polynomials

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#polynomials #radicals #absolute-value #substitution #symmetric-polynomials
250
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Roots of a polynomial : finding the sum of the squares of the product of two roots

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#polynomials #roots #symmetric-polynomials
67
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Find the value of a third order circulant type determinant

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#linear-algebra #matrices #polynomials #determinant #symmetric-polynomials
172
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An algebraic inequality involving $\sum_{cyc} \frac1{(a+2b+3c)^2}$

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#inequality #polynomials #symmetric-polynomials #a.m.-g.m.-inequality #sum-of-squares-method
130
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Show that if $x+y+z=x^2+y^2+z^2=x^3+y^3+z^3=1$ then $xyz=0$

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#algebra-precalculus #polynomials #systems-of-equations #symmetric-polynomials
692
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Form an equation whose roots are $(a-b)^2,(b-c)^2,(c-a)^2.$

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#algebra-precalculus #polynomials #roots #cubics #symmetric-polynomials
66
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Find the value of $\frac{a+b+c}{d+e+f}$

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#systems-of-equations #quadratics #symmetric-polynomials
505
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Equation System with 4 real variables

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#linear-algebra #polynomials #systems-of-equations #real-numbers #symmetric-polynomials
72
Views

How can I prove the following equality given two constraints?

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#algebra-precalculus #polynomials #symmetric-polynomials
169
Views

Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.

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#inequality #optimization #maxima-minima #symmetric-polynomials #cauchy-schwarz-inequality
319
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Given a set of polynomials that correspond to weak compositions of an integer, are all possible products of d such polynomials linearly independent?

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#linear-algebra #combinatorics #vector-spaces #symmetric-polynomials
75
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Find real and distinct solutions

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#systems-of-equations #symmetric-polynomials
91
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A simple problem with a simple and a nonsimple solution

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#polynomials #symmetric-polynomials
192
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Prove that $\sqrt{x^2+yz}+\sqrt{y^2+xz}+\sqrt{z^2+xy} \le 3$

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#inequality #polynomials #radicals #symmetric-polynomials #cauchy-schwarz-inequality
108
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How can I solve this system of equations??

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#systems-of-equations #symmetric-polynomials

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