Question

Show the following inequality.

score 128 · Answer 1 · 2026-03-22 15:29:14

128

Views

Show the following inequality.

Published on 22 Mar 2026 - 15:29

score 486 · Answer 2 · 2026-03-22 23:02:20

486

Views

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

Published on 22 Mar 2026 - 23:02

score 156 · Answer 3 · 2026-03-22 22:01:55

156

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 22 Mar 2026 - 22:01

score 121 · Answer 4 · 2026-03-24 03:47:12

121

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 24 Mar 2026 - 3:47

score 105 · Answer 5 · 2026-03-21 10:42:38

105

Views

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

Published on 21 Mar 2026 - 10:42

score 611 · Answer 6 · 2026-03-24 16:38:26

611

Views

A better way to prove this inequality

Published on 24 Mar 2026 - 16:38

score 109 · Answer 7 · 2026-03-22 19:31:59

109

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 22 Mar 2026 - 19:31

score 113 · Answer 8 · 2026-03-24 11:12:42

113

Views

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

Published on 24 Mar 2026 - 11:12

score 96 · Answer 9 · 2026-03-24 01:49:54

96

Views

Proving the following inequality without using AM-GM inequality.

Published on 24 Mar 2026 - 1:49

score 126 · Answer 10 · 2026-03-23 04:12:39

126

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 23 Mar 2026 - 4:12

score 209 · Answer 11 · 2026-03-22 13:47:36

209

Views

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

Published on 22 Mar 2026 - 13:47

score 570 · Answer 12 · 2026-03-17 07:38:00

570

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 17 Mar 2026 - 7:38

score 290 · Answer 13 · 2026-03-17 11:38:09

290

Views

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

Published on 17 Mar 2026 - 11:38

score 54 · Answer 14 · 2026-03-17 12:12:21

54

Views

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

Published on 17 Mar 2026 - 12:12

score 56 · Answer 15 · 2026-03-22 22:11:14

56

Views

Prove using squared number property

Published on 22 Mar 2026 - 22:11

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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