Question

Given three non-negatve numbers $a,b,c$. Prove that $1+a^{2}+b^{2}+c^{2}+4abc\geqq a+b+c+ab+bc+ca$ .

score 295 · Answer 1 · 2026-03-25 06:06:19

295

Views

Given three non-negatve numbers $a,b,c$. Prove that $1+a^{2}+b^{2}+c^{2}+4abc\geqq a+b+c+ab+bc+ca$ .

Published on 25 Mar 2026 - 6:06

score 177 · Answer 2 · 2026-03-24 23:46:38

177

Views

Given three non-negative numbers $a,b,c$ so that $a+b+c=3$. Prove that $\prod\limits_{cyc}(\!2+ a^{2}\!)+abc\geqq 28$ .

Published on 24 Mar 2026 - 23:46

score 51 · Answer 3 · 2019-04-24 23:34:18

51

Views

Solving Higher Order Differential Equations

Published on 24 Apr 2019 - 23:34

score 157 · Answer 4 · 2019-04-27 01:21:57

157

Views

Antiderivative of $(1+x^3)^{-1/3}$.

Published on 27 Apr 2019 - 1:21

score 268 · Answer 5 · 2026-03-25 19:05:08

268

Views

How can I determine the form of a geometric series in a recurrence relation by using iterative substitution?

Published on 25 Mar 2026 - 19:05

score 210 · Answer 6 · 2019-04-30 04:03:18

210

Views

Value of $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}+\frac{1}{\sqrt{1+d^2}}$

Published on 30 Apr 2019 - 4:03

score 127 · Answer 7 · 2026-03-25 06:12:57

127

Views

Prove that $\sum_\text{cyc}\frac{a}{b^2}\ge 3\sum_{cyc}\frac{1}{a^2}$ for $a,b,c>0$ such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$

Published on 25 Mar 2026 - 6:12

score 125 · Answer 8 · 2019-05-01 05:47:49

125

Views

How do i integrate $\int \frac{dx}{(2x+3)\sqrt{(x^2+3x+2})}$?

Published on 01 May 2019 - 5:47

score 122 · Answer 9 · 2026-03-25 06:06:58

122

Views

Prove/disprove $\sum_{cyc}a\sqrt{\frac{(ca + 1)(ab + 1)}{bc + 1}} \ge 2$ where $a$, $b$, $c > 0$ and $a^2 + b^2 + c^2 = 1$

Published on 25 Mar 2026 - 6:06

score 86 · Answer 10 · 2019-05-02 05:12:51

86

Views

why is the following U-Substitution wrong?

Published on 02 May 2019 - 5:12

score 268 · Answer 11 · 2019-05-02 20:18:29

268

Views

How to solve $\int^1_{-1} \frac{\sin(x)}{1+x^2}dx$?

Published on 02 May 2019 - 20:18

score 134 · Answer 12 · 2026-03-25 06:13:09

134

Views

Proving $ \sum_{cyc}^{} \frac {a(a^3+b^3)}{a^2+ab+b^2} \ge \frac{2}{3} (a^2+b^2+c^2)$ for $a, b, c > 0$

Published on 25 Mar 2026 - 6:13

score 103 · Answer 13 · 2026-03-25 06:12:11

103

Views

A hard inequality $(a^2-ab+b^2 )(b^2-bc+c^2 )(c^2-ca+a^2 ) + 11abc \leq 12$

Published on 25 Mar 2026 - 6:12

score 144 · Answer 14 · 2026-03-25 07:42:52

144

Views

Find maximum of function $A=\sum _{cyc}\frac{1}{a^2+2}$

Published on 25 Mar 2026 - 7:42

score 312 · Answer 15 · 2026-03-25 06:13:02

312

Views

Inequality for $a,b,c>0$ $\sum_{cyc}\sqrt{\frac{a^3}{14a^2+4b^2}}\leq \sum_{cyc}\sqrt{\frac{a+b}{36}}$

Published on 25 Mar 2026 - 6:13

List Question

Given three non-negatve numbers $a,b,c$. Prove that $1+a^{2}+b^{2}+c^{2}+4abc\geqq a+b+c+ab+bc+ca$ .

Given three non-negative numbers $a,b,c$ so that $a+b+c=3$. Prove that $\prod\limits_{cyc}(\!2+ a^{2}\!)+abc\geqq 28$ .

Solving Higher Order Differential Equations

Antiderivative of $(1+x^3)^{-1/3}$.

How can I determine the form of a geometric series in a recurrence relation by using iterative substitution?

Value of $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}+\frac{1}{\sqrt{1+d^2}}$

Prove that $\sum_\text{cyc}\frac{a}{b^2}\ge 3\sum_{cyc}\frac{1}{a^2}$ for $a,b,c>0$ such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$

How do i integrate $\int \frac{dx}{(2x+3)\sqrt{(x^2+3x+2})}$?

Prove/disprove $\sum_{cyc}a\sqrt{\frac{(ca + 1)(ab + 1)}{bc + 1}} \ge 2$ where $a$, $b$, $c > 0$ and $a^2 + b^2 + c^2 = 1$

why is the following U-Substitution wrong?

How to solve $\int^1_{-1} \frac{\sin(x)}{1+x^2}dx$?

Proving $ \sum_{cyc}^{} \frac {a(a^3+b^3)}{a^2+ab+b^2} \ge \frac{2}{3} (a^2+b^2+c^2)$ for $a, b, c > 0$

A hard inequality $(a^2-ab+b^2 )(b^2-bc+c^2 )(c^2-ca+a^2 ) + 11abc \leq 12$

Find maximum of function $A=\sum _{cyc}\frac{1}{a^2+2}$

Inequality for $a,b,c>0$ $\sum_{cyc}\sqrt{\frac{a^3}{14a^2+4b^2}}\leq \sum_{cyc}\sqrt{\frac{a+b}{36}}$

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