Question

Prove this Hard inequality to CS or AM-GM?

score 159 · Answer 1 · 2026-03-20 14:47:31

159

Views

Prove this Hard inequality to CS or AM-GM?

Published on 20 Mar 2026 - 14:47

score 115 · Answer 2 · 2026-03-17 03:50:50

115

Views

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

Published on 17 Mar 2026 - 3:50

score 46 · Answer 3 · 2026-03-25 06:31:56

46

Views

Find X and Y given two equal terms

Published on 25 Mar 2026 - 6:31

score 55 · Answer 4 · 2026-03-25 01:20:39

55

Views

How to prove that $\frac 1{q_{n+2}}\leq \left|p_{n}-bq_n\right|$?

Published on 25 Mar 2026 - 1:20

score 56 · Answer 5 · 2026-03-25 01:18:33

56

Views

How to prove that $x=\frac{p_n+p_{n-1}x_{n+1}}{p_n+p_{n-1}x_{n+1}}$

Published on 25 Mar 2026 - 1:18

score 157 · Answer 6 · 2018-03-31 02:09:52

157

Views

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

Published on 31 Mar 2018 - 2:09

score 146 · Answer 7 · 2026-03-25 14:25:26

146

Views

Minimum of $\frac{x}{\sqrt{1-x^2}}+\frac{y}{\sqrt{1-y^2}}+\frac{z}{\sqrt{1-z^2}}$

Published on 25 Mar 2026 - 14:25

score 71 · Answer 8 · 2018-04-03 10:33:18

71

Views

Can someone explain if this is a different function?

Published on 03 Apr 2018 - 10:33

score 260 · Answer 9 · 2026-03-25 04:42:44

260

Views

Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$

Published on 25 Mar 2026 - 4:42

score 119 · Answer 10 · 2026-03-25 01:18:29

119

Views

What is the dimension of the set generated by $z \mapsto z + 1$ and $z \mapsto \frac{z}{1+z}$?

Published on 25 Mar 2026 - 1:18

score 531 · Answer 11 · 2026-03-25 13:57:09

531

Views

Prove this inequality $\sum_{cyc}\sqrt[4]{\frac{a}{b+c}}\ge \sqrt[4]{16+\frac{196abc}{(a+b)(b+c)(c+a)}}$

Published on 25 Mar 2026 - 13:57

score 65 · Answer 12 · 2026-03-22 16:54:39

65

Views

Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Published on 22 Mar 2026 - 16:54

score 131 · Answer 13 · 2026-03-25 07:43:14

131

Views

Proving expression$\geq 2$, where variables are $x,y,z$

Published on 25 Mar 2026 - 7:43

score 560 · Answer 14 · 2026-03-25 13:58:09

560

Views

Math Olympiad exercise $\frac{x}{\sqrt{3x+2y+z}}+\frac{y}{\sqrt{3y+2z+x}}+\frac{z}{\sqrt{3z+2x+y}}\leq\sqrt{\frac{x+y+z}{2}}$

Published on 25 Mar 2026 - 13:58

score 48 · Answer 15 · 2018-04-06 09:32:51

48

Views

Fraction simplification numerator unclear

Published on 06 Apr 2018 - 9:32

List Question

Prove this Hard inequality to CS or AM-GM?

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

Find X and Y given two equal terms

How to prove that $\frac 1{q_{n+2}}\leq \left|p_{n}-bq_n\right|$?

How to prove that $x=\frac{p_n+p_{n-1}x_{n+1}}{p_n+p_{n-1}x_{n+1}}$

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

Minimum of $\frac{x}{\sqrt{1-x^2}}+\frac{y}{\sqrt{1-y^2}}+\frac{z}{\sqrt{1-z^2}}$

Can someone explain if this is a different function?

Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$

What is the dimension of the set generated by $z \mapsto z + 1$ and $z \mapsto \frac{z}{1+z}$?

Prove this inequality $\sum_{cyc}\sqrt[4]{\frac{a}{b+c}}\ge \sqrt[4]{16+\frac{196abc}{(a+b)(b+c)(c+a)}}$

Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Proving expression$\geq 2$, where variables are $x,y,z$

Math Olympiad exercise $\frac{x}{\sqrt{3x+2y+z}}+\frac{y}{\sqrt{3y+2z+x}}+\frac{z}{\sqrt{3z+2x+y}}\leq\sqrt{\frac{x+y+z}{2}}$

Fraction simplification numerator unclear

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