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20h
comment prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$
Jineon Baek’s hint works for both the inequalities you want to prove in your idea.
20h
comment prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$
@Macavity $f(x)=\frac{(1-4x)^2(1+3x)}{36(1-x)}$
21h
revised Prove that: $\sum \frac{a^2+2bc}{(b+c)^2}\geq \sum \frac{3}{2}\frac{a}{b+c}$
added 32 characters in body
1d
accepted Is there a probabilistic proof of the inequality $4p(1-p) \leq 1$ for a probability $p$?
1d
answered Prove that: $\sum \frac{a^2+2bc}{(b+c)^2}\geq \sum \frac{3}{2}\frac{a}{b+c}$
2d
comment Does there exist a pair $(i,j)$ such that $x_{i}(1-x_{j})$ and $x_{j}(1-x_{i})$ are not greater than $\frac{1}{4\cos^{2}\frac{\pi}{n+1}}$?
Where did you get this problem from ?
2d
comment Does there exist a pair $(i,j)$ such that $x_{i}(1-x_{j})$ and $x_{j}(1-x_{i})$ are not greater than $\frac{1}{4\cos^{2}\frac{\pi}{n+1}}$?
Some context please.
Jul
22
comment Transforming a latin square into a sudoku
A related question : can the addition table modulo 9 be turned into a sudoku by those methods ?
Jul
22
revised How to find a function $\phi(x)$ such that $\sqrt{1+y^2} - \sqrt{1+x^2} \geq \phi(x) (y-x)$ for each $x,y\in \mathbb{R}$
corrected spelling
Jul
21
accepted Discrete Cauchy integral formula : The interior values are always convex combinations of exterior values for harmonic functions?
Jul
20
comment Discrete Cauchy integral formula : The interior values are always convex combinations of exterior values for harmonic functions?
By the way, I think that the $c_i$ are always nonzero, do you have a proof of that also ?
Jul
20
comment Discrete Cauchy integral formula : The interior values are always convex combinations of exterior values for harmonic functions?
The energy argument is magic.
Jul
20
asked Discrete Cauchy integral formula : The interior values are always convex combinations of exterior values for harmonic functions?
Jul
18
answered Help with complicated functional equation
Jul
17
comment A strange puzzle having two possible solutions
Looks like a classical "limit doesn't exist" situation
Jul
17
answered prove $(a+b+c)^n=a^n+b^n+c^n$ if $(a+b+c)^3=a^3+b^3+c^3$
Jul
17
revised How find this P(x) if $ (x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x) $
added 135 characters in body
Jul
17
comment How find this P(x) if $ (x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x) $
@chinamath could you please unaccept this answer, so I can delete it.
Jul
17
revised How find this P(x) if $ (x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x) $
edited body
Jul
17
revised How find this P(x) if $ (x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x) $
edited body