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How to find the minimum of $abcd+\sqrt{(a^2+1)(b^2+1)(c^2+1)(d^2+1)}$ when $ab+bc+cd+da+ac+bd=6$

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#inequality #optimization #maxima-minima #symmetric-polynomials
202
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Lower bound of a constrained 3-variables expression

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#inequality #operator-theory #symmetric-polynomials #positive-semidefinite #contraction-operator
123
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Question: Using the Cauchy-Schwarz Inequality to compare between 2 expressions

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#inequality #summation #cauchy-schwarz-inequality #symmetric-polynomials
60
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A question involving inequality

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#matrices #inequality #proof-writing #symmetric-polynomials
43
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Inequality with a global minimum

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#algebra-precalculus #inequality #symmetric-polynomials
95
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Integer solutions of $\frac{(a+b)(a+c)(b+c)}{2} + (a+b+c)^3 = 1 -abc $

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#elementary-number-theory #diophantine-equations #symmetric-polynomials
455
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Barnard and Child inequality exercise

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#inequality #products #symmetric-polynomials #holder-inequality #muirhead-inequality
118
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Let $P(x)=x^5+x^2+1$ and the equation has roots $x_1,x_2,..x_5$.

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#polynomials #symmetric-polynomials
183
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Help understanding why finite Boolean rngs must be rings

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#abstract-algebra #logic #boolean-algebra #symmetric-polynomials #boolean-ring
27
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Number of possibility, up to commutativity, that a sum of $n$ non negative integer numbers is less or equal than $d$.

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#combinatorics #integer-partitions #symmetric-polynomials
88
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Elementary proof for the inequality

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#inequality #proof-writing #cauchy-schwarz-inequality #symmetric-polynomials #sum-of-squares-method
240
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Given that $x_1, x_2, x_3$ are the roots of the polynomial $x^3-2x^2+3x+5=0$ find $(x_2-x_1)^2(x_3-x_1)^2(x_3-x_2)^2$.

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#polynomials #roots #cubics #symmetric-polynomials #discriminant
104
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Find $\lfloor k^4\rfloor$ where $k^3 - 5k^2 + 2 = 0$.

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#calculus #roots #ceiling-and-floor-functions #cubics #symmetric-polynomials
126
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An interesting question of algebraic manipulation

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#algebra-precalculus #summation #symmetric-polynomials
59
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Matrix functions invariant under conjugation by rotations

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#linear-algebra #symmetric-polynomials

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