Question

Prove $\sum\limits_{cyc} \frac{1- x_{1}}{5\,{x_{1}}^{4}- 9\,{x_{1}}^{2}- 450}\geq 0$

score 152 · Answer 1 · 2026-03-25 06:13:12

152

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Prove $\sum\limits_{cyc} \frac{1- x_{1}}{5\,{x_{1}}^{4}- 9\,{x_{1}}^{2}- 450}\geq 0$

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196

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178

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score 525 · Answer 9 · 2018-07-16 13:40:22

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prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

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score 749 · Answer 10 · 2026-03-25 07:44:58

749

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In trig substitutions, why favor $\sin$, $\tan$, $\sec$, $\sinh$, $\cosh$, $\tanh$ over $\cos$, $\cot$, $\csc$, etc?

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score 260 · Answer 11 · 2026-03-25 04:43:22

260

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$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Published on 25 Mar 2026 - 4:43

score 74 · Answer 12 · 2018-07-21 00:10:12

74

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Question about substitutions in the double integral $\int_0^1\int_0^1 \frac{-\ln xy}{1-xy} dx\, dy = 2\zeta(3)$

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69

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score 98 · Answer 14 · 2026-03-22 16:54:05

98

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score 389 · Answer 15 · 2018-07-24 19:51:15

389

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List Question

Prove $\sum\limits_{cyc} \frac{1- x_{1}}{5\,{x_{1}}^{4}- 9\,{x_{1}}^{2}- 450}\geq 0$

Inequality from AMM problems section

What tools one should use for inequalities?

tangent of inverse secant function

Using differentials in integration by substitution

A counterexample to verify that composition is not commutative?

Cylindrical integral transformations

Integral by substitution of an absolute value of a derivative

prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

In trig substitutions, why favor $\sin$, $\tan$, $\sec$, $\sinh$, $\cosh$, $\tanh$ over $\cos$, $\cot$, $\csc$, etc?

$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Question about substitutions in the double integral $\int_0^1\int_0^1 \frac{-\ln xy}{1-xy} dx\, dy = 2\zeta(3)$

Solving of the equation $e^{-x\pi}-2e^{-2x\pi}=0$

Common zeros of two univariate polynomials over $\mathbb{C}(y)$

Issue with $\int_0^{\infty}\frac{\cos(x^2)}{x^2}dx$

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