New posts in sum-of-squares-method

SOS: Proof of the AM-GM inequality

inequality alternative-proof a.m.-g.m.-inequality sum-of-squares-method

Express $x^4 + y^4 + x^2 + y^2$ as sum of squares of three polynomials in $x,y$ [duplicate]

algebra-precalculus polynomials sum-of-squares-method

Polynomial equal to sum of squares of polynomials [duplicate]

algebra-precalculus polynomials sums-of-squares sum-of-squares-method real-algebraic-geometry

How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$

inequality polynomials a.m.-g.m.-inequality sum-of-squares-method rearrangement-inequality

proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$.

inequality substitution a.m.-g.m.-inequality cauchy-schwarz-inequality sum-of-squares-method

Find three polynomials whose squares sum up to $x^4 + y^4 + x^2 + y^2$

polynomials sum-of-squares-method

Given $P(x)=x^{4}-4x^{3}+12x^{2}-24x+24,$ then $P(x)=|P(x)|$ for all real $x$

algebra-precalculus inequality polynomials absolute-value sum-of-squares-method

Sum of Two Squares of a Quartic

polynomials sum-of-squares-method

Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$

inequality radicals lagrange-multiplier sum-of-squares-method tangent-line-method

Choi Lam homogeneous polynomials as sums of squares

number-theory polynomials sum-of-squares-method multivariate-polynomial

symetric inequality for a rational function of three variables

inequality summation sum-of-squares-method

Find parameters $a,b$ such that $x^6-2 x^5+2 x^4+2 x^3-x^2-2 x+1-\left(x^3-x^2+a x+b\right)^2>0$

real-analysis inequality polynomials sum-of-squares-method

Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$

inequality contest-math radicals sum-of-squares-method rearrangement-inequality

Proving $abcd+3\geq a+b+c+d$

algebra-precalculus inequality contest-math sum-of-squares-method

Write $(x^2 + y^2 + z^2)^2 - 3 ( x^3 y + y^3 z + z^3 x)$ as a sum of (three) squares of quadratic forms

matrices polynomials optimization quadratic-forms sum-of-squares-method

Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

inequality summation contest-math radicals sum-of-squares-method

Prove QM-AM inequality

inequality means cauchy-schwarz-inequality jensen-inequality sum-of-squares-method

Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$

inequality contest-math cauchy-schwarz-inequality sum-of-squares-method rearrangement-inequality