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 25 Mar 2026 - 1:18

238

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Move parabola to make it tangent to lines

Published on 24 Mar 2026 - 23:45

2.3k

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Inequalities - Tangent line trick

Published on 10 Apr 2026 - 23:23

396

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Understanding the proof of an inequality

Published on 27 Mar 2026 - 9:55

124

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

Published on 24 Mar 2026 - 23:46

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 25 Mar 2026 - 1:18

68

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Proof of an inequality: is it correct?

Published on 27 Mar 2026 - 10:58

159

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

Published on 24 Mar 2026 - 23:44

136

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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 25 Mar 2026 - 1:18

818

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Find maximum value by using AM-GM inequality

Published on 24 Mar 2026 - 23:41

80

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3-variable symmetric inequality

Published on 10 Apr 2026 - 22:20

152

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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 25 Mar 2026 - 1:20

217

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

Published on 24 Mar 2026 - 23:46

168

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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 25 Mar 2026 - 1:18

170

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Proof of an interesting inequality

Published on 10 Apr 2026 - 20:27

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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