List questions from tangent-line-method

Published on 15 Apr 2026 - 14:05

196

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A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Published on 16 Apr 2026 - 19:40

289

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Inequality with a High Degree Constraint

Published on 11 Apr 2026 - 0:02

84

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Dubious proof of an Inequality

Published on 10 Apr 2026 - 15:47

259

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Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Published on 17 Apr 2026 - 7:46

71

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Is this Factorization?

Published on 25 Mar 2026 - 15:45

158

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cyclic rational inequalities $\frac{1}{a^2+3}+\frac{1}{b^2+3}+\frac{1}{c^2+3}\leq\frac{27}{28}$ when $a+b+c=1$

Published on 17 Apr 2026 - 2:40

164

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Inequality with $\sum a^5+8\sum ab$

Published on 11 Apr 2026 - 6:17

123

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Prove that: $(a^5-2a+4)(b^5-2b+4)(c^5-2c+4)\ge9(ab+bc+ca)$

Published on 17 Apr 2026 - 7:42

252

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Using Rearrangement Inequality .

Published on 25 Mar 2026 - 15:45

282

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Prove or disprove $\sum\limits_{1\le i < j \le n} \frac{x_ix_j}{1-x_i-x_j} \le \frac18$ for $\sum\limits_{i=1}^n x_i = \frac12$($x_i\ge 0, \forall i$)

Published on 16 Apr 2026 - 22:00

List Question

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Inequality with a High Degree Constraint

Dubious proof of an Inequality

Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Is this Factorization?

cyclic rational inequalities $\frac{1}{a^2+3}+\frac{1}{b^2+3}+\frac{1}{c^2+3}\leq\frac{27}{28}$ when $a+b+c=1$

Inequality with $\sum a^5+8\sum ab$

Prove that: $(a^5-2a+4)(b^5-2b+4)(c^5-2c+4)\ge9(ab+bc+ca)$

Using Rearrangement Inequality .

Prove or disprove $\sum\limits_{1\le i < j \le n} \frac{x_ix_j}{1-x_i-x_j} \le \frac18$ for $\sum\limits_{i=1}^n x_i = \frac12$($x_i\ge 0, \forall i$)

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