Question

Algebraic inequality for positive reals $a,b,c$

score 79 · Answer 1 · 2026-03-25 07:42:15

79

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Algebraic inequality for positive reals $a,b,c$

Published on 25 Mar 2026 - 7:42

score 453 · Answer 2 · 2026-03-22 17:05:00

453

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show this inequality with $\sum_{i=1}^{n}a_{i}=n$

Published on 22 Mar 2026 - 17:05

score 439 · Answer 3 · 2019-01-11 05:14:01

439

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Proving that the arithmetic and geometric means of a collection of non-negative numbers lies between their minimum and maximum values

Published on 11 Jan 2019 - 5:14

score 208 · Answer 4 · 2026-03-26 04:14:48

208

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Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Published on 26 Mar 2026 - 4:14

score 109 · Answer 5 · 2019-01-12 02:57:38

109

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Inequality problem: with $x,y,z>0$, show that $\frac{x^5}{y^3}+\frac{y^5}{z^3}+\frac{z^5}{x^3}\geq x^2+y^2+z^2$

Published on 12 Jan 2019 - 2:57

score 384 · Answer 6 · 2019-01-12 12:35:43

384

Views

Finding maxima of a function $f(x) = \sqrt{x} - 2x^2$ without calculus

Published on 12 Jan 2019 - 12:35

score 101 · Answer 7 · 2019-01-14 08:44:00

101

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How to find the range of $y=\frac{x^2+1}{x+1}$ without using derivative?

Published on 14 Jan 2019 - 8:44

score 3.7k · Answer 8 · 2019-01-16 11:40:22

3.7k

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Maximum value of function $f(x)=\frac{x^4-x^2}{x^6+2x^3-1}$ when $x >1$

Published on 16 Jan 2019 - 11:40

score 147 · Answer 9 · 2019-01-17 06:41:46

147

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If $x$ and $y$ are acute, and $\sin y = 3 \cos (x+y) \sin x$⁡, then find the maximum value of $\tan y$

Published on 17 Jan 2019 - 6:41

score 62 · Answer 10 · 2019-01-20 18:59:40

62

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Is this inequality true? $u^2+v^2+s^2+t^2\geq (u+v)(s+t)$

Published on 20 Jan 2019 - 18:59

score 202 · Answer 11 · 2019-01-21 23:49:33

202

Views

How to prove using AM-GM $ \frac{4}{abcd} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} $

Published on 21 Jan 2019 - 23:49

score 172 · Answer 12 · 2026-03-25 09:38:58

172

Views

to prove this inequality $\sum a^3b+3\ge 2(ab+bc+ca)$

Published on 25 Mar 2026 - 9:38

score 47 · Answer 13 · 2019-01-26 11:31:50

47

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Extremes of the function in a certain set

Published on 26 Jan 2019 - 11:31

score 159 · Answer 14 · 2026-03-24 23:44:57

159

Views

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

Published on 24 Mar 2026 - 23:44

score 212 · Answer 15 · 2019-02-04 12:20:23

212

Views

Finding the greatest value of $a^2b^3c^2$ if $a+b+c=3$ and all numbers are positive

Published on 04 Feb 2019 - 12:20

List Question

Algebraic inequality for positive reals $a,b,c$

show this inequality with $\sum_{i=1}^{n}a_{i}=n$

Proving that the arithmetic and geometric means of a collection of non-negative numbers lies between their minimum and maximum values

Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Inequality problem: with $x,y,z>0$, show that $\frac{x^5}{y^3}+\frac{y^5}{z^3}+\frac{z^5}{x^3}\geq x^2+y^2+z^2$

Finding maxima of a function $f(x) = \sqrt{x} - 2x^2$ without calculus

How to find the range of $y=\frac{x^2+1}{x+1}$ without using derivative?

Maximum value of function $f(x)=\frac{x^4-x^2}{x^6+2x^3-1}$ when $x >1$

If $x$ and $y$ are acute, and $\sin y = 3 \cos (x+y) \sin x$⁡, then find the maximum value of $\tan y$

Is this inequality true? $u^2+v^2+s^2+t^2\geq (u+v)(s+t)$

How to prove using AM-GM $ \frac{4}{abcd} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} $

to prove this inequality $\sum a^3b+3\ge 2(ab+bc+ca)$

Extremes of the function in a certain set

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

Finding the greatest value of $a^2b^3c^2$ if $a+b+c=3$ and all numbers are positive

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