New posts in symmetric-polynomials

Inequality of elementary symmetric polynomials

inequality symmetric-polynomials

Ring of polynomials as a module over symmetric polynomials

abstract-algebra algebraic-geometry modules representation-theory symmetric-polynomials

Why does the discriminant of a cubic polynomial being less than $0$ indicate complex roots?

algebra-precalculus polynomials roots symmetric-polynomials

Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ?

polynomials systems-of-equations symmetric-polynomials

Find the value of $\textrm{cosec}^2\left(\frac\pi7\right) +\textrm{cosec}^2\left(\frac{2\pi}7\right)+\textrm{cosec}^2\left(\frac{4\pi}7\right)$

trigonometry symmetric-polynomials

Inequality involving three positive numbers [duplicate]

inequality radicals fractions symmetric-polynomials

Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$

inequality contest-math symmetric-polynomials uvw

Three-variable system of simultaneous equations

algebra-precalculus polynomials systems-of-equations symmetric-polynomials

Using Vieta's theorem for cubic equations to derive the cubic discriminant

algebra-precalculus polynomials roots symmetric-polynomials

For $abc=1$ prove that $\sum\limits_{cyc}\frac{a}{a^{11}+1}\leq\frac{3}{2}.$

multivariable-calculus inequality symmetric-polynomials

Super hard system of equations

algebra-precalculus systems-of-equations symmetric-polynomials

What is the function space generated by addition and $(a,b)\mapsto (a+b)^{-1}\cdot a\cdot b$ of elements and their inverses?

symmetric-polynomials

Rational solutions to $a+b+c=abc=6$

number-theory elementary-number-theory diophantine-equations elliptic-curves symmetric-polynomials

If $x+\frac1x=5$ find $x^5+\frac1{x^5}$.

algebra-precalculus analysis polynomials binomial-coefficients symmetric-polynomials

Is it possible to have three real numbers that have both their sum and product equal to $1$?

algebra-precalculus systems-of-equations symmetric-polynomials

Symmetric polynomials and the Newton identities

abstract-algebra polynomials symmetric-polynomials