List questions from substitution

Published on 31 Oct 2014 - 21:33

458

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How to prove the inequality $ \frac{a}{\sqrt{1+a}}+\frac{b}{\sqrt{1+b}}+\frac{c}{\sqrt{1+c}} \ge \frac{3\sqrt{2}}{2}$

Published on 25 Mar 2026 - 11:21

921

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How prove this $x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$

Published on 20 Mar 2026 - 4:29

292

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How prove this inequality$4(a^2+b^2+c^2)+9a^2b^2c^2\ge 21$

Published on 25 Mar 2026 - 14:23

188

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prove that $a^2 b^2 (a^2 + b^2 - 2) \ge (a + b)(ab - 1)$

Published on 25 Mar 2026 - 12:54

1k

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For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$

Published on 25 Mar 2026 - 7:45

83

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Given three non-negative numbers $a,b,c$. Prove that $\frac{a+b+c}{k}\geqq\sum\limits_{cyc}\frac{a-b}{b+ k}$ for $k= constant$ so that $k> 0$ .

Published on 25 Mar 2026 - 18:08

49

Views

Does there exist a substitution to transform this differential?

Published on 07 Oct 2019 - 6:16

78

Views

Substitution integral with $t=x^3$

Published on 09 Oct 2019 - 0:45

110

Views

Solving a Riccati ODE Twice

Published on 22 Mar 2026 - 10:20

142

Views

Riccati Substitution Formula

Published on 11 Oct 2019 - 4:06

63

Views

Rewrite a non-linear first order differential equation to a linear differential equation

Published on 11 Oct 2019 - 10:54

31

Views

Proving limits using u-substitution

Published on 27 Mar 2026 - 0:54

188

Views

Proving a much stronger version of AM-GM for three variables

Published on 24 Oct 2019 - 13:43

105

Views

How can we attain 3 solutions when using Vieta's Substitution?

Published on 26 Mar 2026 - 11:06

List Question

How to prove $\frac 1{2+a}+\frac 1{2+b}+\frac 1{2+c}\le 1$?

How to prove the inequality $ \frac{a}{\sqrt{1+a}}+\frac{b}{\sqrt{1+b}}+\frac{c}{\sqrt{1+c}} \ge \frac{3\sqrt{2}}{2}$

How prove this $x^3+y^3+z^3+3\ge 2(x^2+y^2+z^2)$

How prove this inequality$4(a^2+b^2+c^2)+9a^2b^2c^2\ge 21$

prove that $a^2 b^2 (a^2 + b^2 - 2) \ge (a + b)(ab - 1)$

For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$

Given three non-negative numbers $a,b,c$. Prove that $\frac{a+b+c}{k}\geqq\sum\limits_{cyc}\frac{a-b}{b+ k}$ for $k= constant$ so that $k> 0$ .

Does there exist a substitution to transform this differential?

Substitution integral with $t=x^3$

Solving a Riccati ODE Twice

Riccati Substitution Formula

Rewrite a non-linear first order differential equation to a linear differential equation

Proving limits using u-substitution

Proving a much stronger version of AM-GM for three variables

How can we attain 3 solutions when using Vieta's Substitution?

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