List questions from tangent-line-method

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If $a$, $b$, $c$ are positive real numbers such that $a^2 + b^2 + c^2 = 27$. Find the least value of $a^3 + b^3 + c^3$?

Published on 16 Nov 2018 - 11:47

237

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Move parabola to make it tangent to lines

Published on 22 Nov 2018 - 2:36

2.3k

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Inequalities - Tangent line trick

Published on 27 Nov 2018 - 20:52

394

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Understanding the proof of an inequality

Published on 28 Nov 2018 - 21:17

123

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Transform parabola to be tangent to line in point and through other point

Published on 02 Dec 2018 - 22:13

1.3k

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Given that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$.Show that:$(a+1)(b+1)(c+1)\ge 64$

Published on 04 Dec 2018 - 20:58

66

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Proof of an inequality: is it correct?

Published on 06 Dec 2018 - 14:06

158

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Show that $a^{2014}+b^{2014}\geq a^{2013}+b^{2013} $.

Published on 26 Jan 2019 - 19:26

135

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Does $\sum\limits_{i=1}^n x_i = 1$ imply $\sum\limits_{i=1}^n x_i^2 \geq \frac{1}{n}$?

Published on 23 Feb 2019 - 19:04

817

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Find maximum value by using AM-GM inequality

Published on 26 Feb 2019 - 6:11

77

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3-variable symmetric inequality

Published on 28 Feb 2019 - 15:50

151

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$\frac{a}{a^a+1}+\frac{b}{b^b+1}+\frac{c}{c^c+1}\leq \frac{3}{2}$ with $abc=1$

Published on 01 Mar 2019 - 13:19

216

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Prove $\sum \sqrt{\frac{a^2}{6a^2+5ab+b^2}}\le \frac{\sqrt{3}}{2}$

Published on 14 Mar 2019 - 14:19

167

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Prove that $(a - 1)^3 + (b - 1)^3 + (c - 1)^3 \ge -\dfrac{3}{4}$ where $a+b+c=3$

Published on 18 Mar 2019 - 14:27

167

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Proof of an interesting inequality

Published on 19 Mar 2019 - 12:26

List Question

If $a$, $b$, $c$ are positive real numbers such that $a^2 + b^2 + c^2 = 27$. Find the least value of $a^3 + b^3 + c^3$?

Move parabola to make it tangent to lines

Inequalities - Tangent line trick

Understanding the proof of an inequality

Transform parabola to be tangent to line in point and through other point

Given that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$.Show that:$(a+1)(b+1)(c+1)\ge 64$

Proof of an inequality: is it correct?

Show that $a^{2014}+b^{2014}\geq a^{2013}+b^{2013} $.

Does $\sum\limits_{i=1}^n x_i = 1$ imply $\sum\limits_{i=1}^n x_i^2 \geq \frac{1}{n}$?

Find maximum value by using AM-GM inequality

3-variable symmetric inequality

$\frac{a}{a^a+1}+\frac{b}{b^b+1}+\frac{c}{c^c+1}\leq \frac{3}{2}$ with $abc=1$

Prove $\sum \sqrt{\frac{a^2}{6a^2+5ab+b^2}}\le \frac{\sqrt{3}}{2}$

Prove that $(a - 1)^3 + (b - 1)^3 + (c - 1)^3 \ge -\dfrac{3}{4}$ where $a+b+c=3$

Proof of an interesting inequality

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