Question

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

score 232 · Answer 1 · 2026-03-19 19:54:23

232

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How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

Published on 19 Mar 2026 - 19:54

score 125 · Answer 2 · 2026-03-25 06:18:51

125

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Difference of 2 roots

Published on 25 Mar 2026 - 6:18

score 3k · Answer 3 · 2026-03-17 12:16:34

3k

Views

The complex equation $x^3 = 9 + 46i$ has a solution of the form $a + bi$ where $a,b\in \mathbb Z$. Find the value of $a^3 + b^3$

Published on 17 Mar 2026 - 12:16

score 7.8k · Answer 4 · 2026-03-23 00:43:08

7.8k

Views

Solving $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$? (1983 AIME problem 3)

Published on 23 Mar 2026 - 0:43

score 793 · Answer 5 · 2026-03-22 21:14:53

793

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Hidden variable resultant for solution of a system of polynomial equations

Published on 22 Mar 2026 - 21:14

score 221 · Answer 6 · 2026-03-24 23:49:54

221

Views

Is $\phi: \mathbb{F_p}(X) \rightarrow \mathbb{F_p}(X), a \mapsto a$ for $a \in \mathbb{F_p}$ and $X \mapsto X+1$ a field homomorphism?

Published on 24 Mar 2026 - 23:49

score 340 · Answer 7 · 2026-03-24 09:26:47

340

Views

If some four of given five distinct points in projective plane are collinear , then there are more than one conic passing through the five points

Published on 24 Mar 2026 - 9:26

score 357 · Answer 8 · 2026-03-25 11:11:55

357

Views

If $\lambda$ is an eigenvalue for a linear operator $T(x)$ and if $g(t)$ is a polynomial, then $g(T(x)) = g(\lambda)x$

Published on 25 Mar 2026 - 11:11

score 1.2k · Answer 9 · 2026-03-23 02:01:26

1.2k

Views

Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$

Published on 23 Mar 2026 - 2:01

score 84 · Answer 10 · 2018-01-24 04:53:20

84

Views

Do we have non algebraic solution for arbitrary nth degree polynomial?

Published on 24 Jan 2018 - 4:53

score 80 · Answer 11 · 2026-03-22 08:30:29

80

Views

Is it possible to construct a compact operator $A$ such that all polynomials of degree $1$ are in the nullspace of $I-A$?

Published on 22 Mar 2026 - 8:30

score 919 · Answer 12 · 2026-03-22 23:23:00

919

Views

How is symmetry in an inequality determined?

Published on 22 Mar 2026 - 23:23

score 337 · Answer 13 · 2026-03-25 07:46:06

337

Views

space of d variate polynomial of degree at most n restricted to a manifold in R^d

Published on 25 Mar 2026 - 7:46

score 915 · Answer 14 · 2026-03-22 22:52:50

915

Views

How can one prove that this polynomial is non-negative?

Published on 22 Mar 2026 - 22:52

score 123 · Answer 15 · 2018-01-24 14:13:08

123

Views

Find $a$ so that $a \in R, x^4+4x^3+ax^2+4x+1=0$ has all roots in $R$.

Published on 24 Jan 2018 - 14:13

List Question

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

Difference of 2 roots

The complex equation $x^3 = 9 + 46i$ has a solution of the form $a + bi$ where $a,b\in \mathbb Z$. Find the value of $a^3 + b^3$

Solving $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$? (1983 AIME problem 3)

Hidden variable resultant for solution of a system of polynomial equations

Is $\phi: \mathbb{F_p}(X) \rightarrow \mathbb{F_p}(X), a \mapsto a$ for $a \in \mathbb{F_p}$ and $X \mapsto X+1$ a field homomorphism?

If some four of given five distinct points in projective plane are collinear , then there are more than one conic passing through the five points

If $\lambda$ is an eigenvalue for a linear operator $T(x)$ and if $g(t)$ is a polynomial, then $g(T(x)) = g(\lambda)x$

Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$

Do we have non algebraic solution for arbitrary nth degree polynomial?

Is it possible to construct a compact operator $A$ such that all polynomials of degree $1$ are in the nullspace of $I-A$?

How is symmetry in an inequality determined?

space of d variate polynomial of degree at most n restricted to a manifold in R^d

How can one prove that this polynomial is non-negative?

Find $a$ so that $a \in R, x^4+4x^3+ax^2+4x+1=0$ has all roots in $R$.

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