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Prove: $\sqrt[3]{\frac{a^{2}+bc}{b^2+c^2}}+\sqrt[3]{\frac{b^{2}+ac}{a^2+c^2}}+\sqrt[3]{\frac{c^{2}+ab}{a^2+b^2}}\geq 9\frac{\sqrt[3]{abc}}{a+b+c}$
inequality
Proof of an inequality that seems intuitive
inequality
how prove this inequality $\sum\limits_{1\le i<j\le n}|z_{i}-z_{j}|\le n\cot{\frac{\pi}{2n}}$
inequality
upper bounding alternating binomial sums
combinatorics
inequality
summation
binomial-coefficients
Intersection of $n+k$ subspaces of $\mathbb{R}^n$
linear-algebra
inequality
convex-analysis
euclidean-geometry
How do you find (continuous) bounds on the matrix exponential
linear-algebra
matrices
inequality
matrix-exponential
Prove by induction $\frac{n^n}{3^n}<n!<\frac{n^n}{2^n}$ [closed]
inequality
induction
factorial
How prove this inequality $\sum\limits_{cyc}\frac{x^a\ln{x}}{(x^a+y+z)^2}\ge 0$
inequality
Proving an inequality about the product of integrals
calculus
inequality
prove that : $\frac{a^2+b^2}{a+b} + \frac{b^2+c^2}{b+c}+ \frac{c^2+a^2}{c+a} \geq 3$
inequality
How are inequalities from IMO built?
algebra-precalculus
inequality
contest-math
Eigenvalues of $MA$ versus eigenvalues of $A$ for orthogonal projection $M$
linear-algebra
matrices
inequality
proof-verification
eigenvalues-eigenvectors
Unconventional Inequality $ \frac{x^x}{|x-y|}+\frac{y^y}{|y-z|}+\frac{z^z}{|z-x|} > \frac72$
inequality
Parallelogram / Polarization Inequality
real-analysis
functional-analysis
multivariable-calculus
inequality
hilbert-spaces
On odd perfect numbers $n$ and $\sigma\left(n^\lambda\right)$
elementary-number-theory
inequality
divisor-sum
perfect-numbers
An inverse question inspired by Cauchy–Schwarz inequality [duplicate]
real-analysis
sequences-and-series
inequality
Pretty conjecture $x^{\left(\frac{y}{x}\right)^n}+y^{\left(\frac{x}{y}\right)^n}\leq 1$
derivatives
inequality
examples-counterexamples
exponentiation
conjectures
Derivation of bound on expression involving binomial coefficient from Erdős and Rényi 1959
inequality
binomial-coefficients
Prove the inequality and limitation
calculus
inequality
Kind of converse of Kolmogorov maximal inequality
probability
probability-theory
inequality
stochastic-processes
martingales
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