New posts in Symmetric Polynomials

Polynomial $x^3-2x^2-3x-4=0$

Prove that $ a^2+b^2+c^2 \le a^3 +b^3 +c^3 $

Prove that for all positives $a, b$ and $c$, $(\sum_{cyc}\frac{c + a}{b})^2 \ge 4(\sum_{cyc}ca)(\sum_{cyc}\frac{1}{b^2})$.

Symmetric rational function is a rational function in the elementary symmetric polynomials.

If a,b,c be roots of $2x^3+x^2+x-1=0$ show that some expression is equal to 16.

Cauchy-Schwarz inequality for $a_1^4 + a_2^4 + \cdots + a_n^4 \geqslant n$

For non-negative reals $a$, $b$, $c$, show that $3(1-a+a^2)(1-b+b^2)(1-c+c^2)\ge(1+abc+a^2b^2c^2)$

Can I solve this other than using Newton's sums or Newton's identities?

System of equations $x^3+y=y^2\ \& \ y^3+z=z^2\ \& \ z^3+x=x^2$

Prove $\sqrt[3]{\frac{(a^4+b^4)(a^4+c^4)(b^4+c^4)}{abc}}\ge \sqrt{\frac{(a^3+bc)(b^3+ca)(c^3+ab)}{1+abc}}$