Question

Show the following inequality.

score 135 · Answer 1 · 2026-05-02 04:48:47

135

Views

Show the following inequality.

Published on 02 May 2026 - 4:48

score 491 · Answer 2 · 2026-04-29 12:50:44

491

Views

Proving that $\frac {1}{3x^2+1}+\frac {1}{3y^2+1}+\frac {1}{3z^2+1}\geq \frac {3}{16 } $

Published on 29 Apr 2026 - 12:50

score 160 · Answer 3 · 2026-04-29 08:58:56

160

Views

Prove the inequality $\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{c}{1+c^2}\le\frac{3\sqrt3}{4}$

Published on 29 Apr 2026 - 8:58

score 128 · Answer 4 · 2026-04-29 12:50:55

128

Views

Prove the inequality $\left(1+\frac{1}{a_1(1+a_1)}\right)...\left(1+\frac{1}{a_k(1+a_k)}\right)\ge\left(1+\frac{1}{p(1+p)}\right)^k$

Published on 29 Apr 2026 - 12:50

score 113 · Answer 5 · 2026-04-29 12:16:07

113

Views

Let $\sum\frac{1}{a^3+1}=2$. Prove that $\sum\frac{1-a}{a^2-a+1}\ge 0$

Published on 29 Apr 2026 - 12:16

score 617 · Answer 6 · 2026-05-10 11:42:56

617

Views

A better way to prove this inequality

Published on 10 May 2026 - 11:42

score 114 · Answer 7 · 2026-04-29 12:51:14

114

Views

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Published on 29 Apr 2026 - 12:51

score 118 · Answer 8 · 2026-05-02 10:10:51

118

Views

Prove: $2^{a}+ 2^{b}+ 2^{c}\leqq 3$

Published on 02 May 2026 - 10:10

score 101 · Answer 9 · 2026-05-02 12:53:00

101

Views

Proving the following inequality without using AM-GM inequality.

Published on 02 May 2026 - 12:53

score 133 · Answer 10 · 2026-05-03 10:16:45

133

Views

$\frac{a^2} {1+a^2} + \frac{b^2} {1+b^2} + \frac{c^2} {1+c^2} = 2.$ Prove $\frac{a} {1+a^2} + \frac{b} {1+b^2} + \frac{c} {1+c^2} \leq \sqrt{2}.$

Published on 03 May 2026 - 10:16

score 216 · Answer 11 · 2026-05-02 10:07:21

216

Views

Prove that: $\sum\limits_{cyc}\frac{1}{(b+c)^2+a^2}\leq \frac{3}{5}$

Published on 02 May 2026 - 10:07

score 576 · Answer 12 · 2026-05-03 07:02:36

576

Views

Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Published on 03 May 2026 - 7:02

score 296 · Answer 13 · 2026-05-02 10:07:14

296

Views

Monotonicity of the function $(1+x)^{\frac{1}{x}}\left(1+\frac{1}{x}\right)^x$.

Published on 02 May 2026 - 10:07

score 61 · Answer 14 · 2026-05-02 11:36:05

61

Views

Geometry proof of an ratio related problem by a random tangent to a pair of fixed parallel tangents on an ellipse

Published on 02 May 2026 - 11:36

score 62 · Answer 15 · 2026-05-04 02:22:31

62

Views

Prove using squared number property

Published on 04 May 2026 - 2:22

List Question

Show the following inequality.

Proving that $\frac {1}{3x^2+1}+\frac {1}{3y^2+1}+\frac {1}{3z^2+1}\geq \frac {3}{16 } $

Prove the inequality $\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{c}{1+c^2}\le\frac{3\sqrt3}{4}$

Prove the inequality $\left(1+\frac{1}{a_1(1+a_1)}\right)...\left(1+\frac{1}{a_k(1+a_k)}\right)\ge\left(1+\frac{1}{p(1+p)}\right)^k$

Let $\sum\frac{1}{a^3+1}=2$. Prove that $\sum\frac{1-a}{a^2-a+1}\ge 0$

A better way to prove this inequality

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Prove: $2^{a}+ 2^{b}+ 2^{c}\leqq 3$

Proving the following inequality without using AM-GM inequality.

$\frac{a^2} {1+a^2} + \frac{b^2} {1+b^2} + \frac{c^2} {1+c^2} = 2.$ Prove $\frac{a} {1+a^2} + \frac{b} {1+b^2} + \frac{c} {1+c^2} \leq \sqrt{2}.$

Prove that: $\sum\limits_{cyc}\frac{1}{(b+c)^2+a^2}\leq \frac{3}{5}$

Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Monotonicity of the function $(1+x)^{\frac{1}{x}}\left(1+\frac{1}{x}\right)^x$.

Geometry proof of an ratio related problem by a random tangent to a pair of fixed parallel tangents on an ellipse

Prove using squared number property

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