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 240 · Answer 1 · 2026-05-07 18:27:05

240

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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 07 May 2026 - 18:27

score 138 · Answer 2 · 2026-05-10 12:30:49

138

Views

Difference of 2 roots

Published on 10 May 2026 - 12:30

score 3k · Answer 3 · 2026-05-05 00:32:06

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 05 May 2026 - 0:32

score 7.8k · Answer 4 · 2026-04-29 12:26:03

7.8k

Views

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

Published on 29 Apr 2026 - 12:26

score 799 · Answer 5 · 2026-05-10 13:49:05

799

Views

Hidden variable resultant for solution of a system of polynomial equations

Published on 10 May 2026 - 13:49

score 225 · Answer 6 · 2026-05-10 12:35:37

225

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 10 May 2026 - 12:35

score 348 · Answer 7 · 2026-05-05 14:04:26

348

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 05 May 2026 - 14:04

score 360 · Answer 8 · 2026-05-10 15:45:31

360

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 10 May 2026 - 15:45

score 1.2k · Answer 9 · 2026-05-02 18:32:45

1.2k

Views

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

Published on 02 May 2026 - 18:32

score 87 · Answer 10 · 2026-04-11 18:47:04

87

Views

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

Published on 11 Apr 2026 - 18:47

score 87 · Answer 11 · 2026-05-10 15:08:26

87

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 10 May 2026 - 15:08

score 923 · Answer 12 · 2026-04-20 16:31:31

923

Views

How is symmetry in an inequality determined?

Published on 20 Apr 2026 - 16:31

score 340 · Answer 13 · 2026-05-10 13:51:29

340

Views

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

Published on 10 May 2026 - 13:51

score 925 · Answer 14 · 2026-05-10 15:39:39

925

Views

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

Published on 10 May 2026 - 15:39

score 128 · Answer 15 · 2026-04-29 12:29:08

128

Views

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

Published on 29 Apr 2026 - 12:29

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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