Question

Show: $\|u_n\|_X \leq \gamma^{n-1} \|u_0\|_X \quad \forall n \geq 1$

score 51 · Answer 1 · 2026-05-11 04:23:41

51

Views

Show: $\|u_n\|_X \leq \gamma^{n-1} \|u_0\|_X \quad \forall n \geq 1$

Published on 11 May 2026 - 4:23

score 582 · Answer 2 · 2026-05-10 23:31:35

582

Views

If $p$, $q$, $r$ and $s$ are four sides of a quadrilateral, then find the minimum value of $\frac{p^2+ q^2 + r^2}{s^2}$ with logic

Published on 10 May 2026 - 23:31

score 66 · Answer 3 · 2026-05-10 23:20:39

66

Views

Problem in a question concerning Geometric progression and quadratic equations

Published on 10 May 2026 - 23:20

score 111 · Answer 4 · 2026-04-09 07:32:28

111

Views

Inequality for optimization.

Published on 09 Apr 2026 - 7:32

score 169 · Answer 5 · 2026-04-15 11:21:02

169

Views

Find minimum value of $P=\sum \frac{a}{a^2+b^3}$

Published on 15 Apr 2026 - 11:21

score 76 · Answer 6 · 2026-05-10 18:59:37

76

Views

How to prove inequality $a^{\frac{1}{b}}+b^{\frac{1}{a}}\leq \frac {1}{2}$ if $0 <a,b < 1$ and $a+b=1$?

Published on 10 May 2026 - 18:59

score 118 · Answer 7 · 2026-04-16 00:41:31

118

Views

Prove that $\sum \frac {xy}{\sqrt{ (x^2+z^2)(y^2+z^2)}}\leq \frac {3}{2} $

Published on 16 Apr 2026 - 0:41

score 138 · Answer 8 · 2026-04-13 14:32:59

138

Views

AM-GM inequality in $3$ variables

Published on 13 Apr 2026 - 14:32

score 159 · Answer 9 · 2026-04-16 21:19:51

159

Views

Given a positive number $t$, prove that $7>\frac{4t^{3}+56t^{2}+191t+188}{\sqrt{t^{2}+2t+8}\left (7\sqrt{t^{2}+2t+8}+2(6t-2+t^{2})\right )}$ .

Published on 16 Apr 2026 - 21:19

score 78 · Answer 10 · 2026-04-13 23:07:25

78

Views

AM-GM inequality in $n$ variables

Published on 13 Apr 2026 - 23:07

score 94 · Answer 11 · 2026-05-10 19:48:43

94

Views

Inequality of integral : $\int_0^{1}((\sqrt{3}f(x))^{2}-2(f(x)^{3})dx≤1$

Published on 10 May 2026 - 19:48

score 184 · Answer 12 · 2026-05-10 15:03:19

184

Views

$\frac{3(a + b + c)^2}{25(ab + bc + ca)(a^2 + b^2 + c^2)} \le \sum_{cyc}\frac{1}{(3a + b + c)(c + 4a)} \le \frac{\sqrt{3(ab + bc + ca)}}{25abc}$

Published on 10 May 2026 - 15:03

score 250 · Answer 13 · 2026-04-15 19:57:25

250

Views

Find the minimum $K$ such that $\sum_{cyc} \frac{a}{\sqrt{a+b}} \leq K\sqrt{a+b+c}$

Published on 15 Apr 2026 - 19:57

score 289 · Answer 14 · 2026-04-17 11:55:16

289

Views

Prove that $(abc+xyz) \left(\frac{1}{ay}+\frac{1}{bz}+\frac{1}{cx}\right)\geq3$

Published on 17 Apr 2026 - 11:55

score 115 · Answer 15 · 2026-05-10 15:39:41

115

Views

minimum value of $\frac{x}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}$ is

Published on 10 May 2026 - 15:39

List Question

Show: $\|u_n\|_X \leq \gamma^{n-1} \|u_0\|_X \quad \forall n \geq 1$

If $p$, $q$, $r$ and $s$ are four sides of a quadrilateral, then find the minimum value of $\frac{p^2+ q^2 + r^2}{s^2}$ with logic

Problem in a question concerning Geometric progression and quadratic equations

Inequality for optimization.

Find minimum value of $P=\sum \frac{a}{a^2+b^3}$

How to prove inequality $a^{\frac{1}{b}}+b^{\frac{1}{a}}\leq \frac {1}{2}$ if $0 <a,b < 1$ and $a+b=1$?

Prove that $\sum \frac {xy}{\sqrt{ (x^2+z^2)(y^2+z^2)}}\leq \frac {3}{2} $

AM-GM inequality in $3$ variables

Given a positive number $t$, prove that $7>\frac{4t^{3}+56t^{2}+191t+188}{\sqrt{t^{2}+2t+8}\left (7\sqrt{t^{2}+2t+8}+2(6t-2+t^{2})\right )}$ .

AM-GM inequality in $n$ variables

Inequality of integral : $\int_0^{1}((\sqrt{3}f(x))^{2}-2(f(x)^{3})dx≤1$

$\frac{3(a + b + c)^2}{25(ab + bc + ca)(a^2 + b^2 + c^2)} \le \sum_{cyc}\frac{1}{(3a + b + c)(c + 4a)} \le \frac{\sqrt{3(ab + bc + ca)}}{25abc}$

Find the minimum $K$ such that $\sum_{cyc} \frac{a}{\sqrt{a+b}} \leq K\sqrt{a+b+c}$

Prove that $(abc+xyz) \left(\frac{1}{ay}+\frac{1}{bz}+\frac{1}{cx}\right)\geq3$

minimum value of $\frac{x}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}$ is

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