List questions from a-m-g-m-inequality

Published on 14 Apr 2022 - 14:40

52

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question based on AM/GM

Published on 15 Apr 2022 - 1:43

557

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Proving the AM-GM Inequality by induction

Published on 15 Apr 2022 - 7:56

36

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Prove the A.M.-G.M. inequality for n terms using induction

Published on 17 Apr 2022 - 11:20

104

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To prove the given inequality of n numbers

Published on 22 Apr 2022 - 12:05

51

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To prove the following inequality of real numbers

Published on 22 Apr 2022 - 14:42

111

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To prove the following inequalities of positive rational numbers

Published on 25 Mar 2026 - 19:12

150

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How can I prove that, if $x,y,z>0$ and $xyz=1$, then $2(x^2+y^2+z^2)+9\geq 5(x+y+z)$

Published on 24 Apr 2022 - 13:41

87

Views

Proving $\frac{x^2+y^2+z^2}{x+y+z}+\frac 32\sqrt[3]\frac{xy+yz+xz}{x+y+z}\geq \frac 52$, for positive values with $xyz=1$, without expansion?

Published on 24 Apr 2022 - 23:08

108

Views

How would I prove the following using the AGM inequality?

Published on 25 Apr 2022 - 15:30

66

Views

Is there a solution for $(\frac{3}{x+y+z})^n+(\frac{3}{x+y+z})^{5-n}<2$?

Published on 25 Apr 2022 - 17:30

62

Views

To prove the inequality of positive rational numbers

Published on 01 May 2022 - 15:58

124

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find the maximum of $x+\frac{1}{2y}$ under the condition $(2xy-1)^2=(5y+2)(y-2)$

Published on 02 May 2022 - 1:25

20

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Inequality of positive integers

Published on 08 May 2022 - 15:16

90

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How can I prove that the perimeter is at most 60?

Published on 12 May 2022 - 11:41

List Question

Solve the inequality $ \sum_{cyc}\frac{a-bc}{a+bc} \le \frac32$

question based on AM/GM

Proving the AM-GM Inequality by induction

Prove the A.M.-G.M. inequality for n terms using induction

To prove the given inequality of n numbers

To prove the following inequality of real numbers

To prove the following inequalities of positive rational numbers

How can I prove that, if $x,y,z>0$ and $xyz=1$, then $2(x^2+y^2+z^2)+9\geq 5(x+y+z)$

Proving $\frac{x^2+y^2+z^2}{x+y+z}+\frac 32\sqrt[3]\frac{xy+yz+xz}{x+y+z}\geq \frac 52$, for positive values with $xyz=1$, without expansion?

How would I prove the following using the AGM inequality?

Is there a solution for $(\frac{3}{x+y+z})^n+(\frac{3}{x+y+z})^{5-n}<2$?

To prove the inequality of positive rational numbers

find the maximum of $x+\frac{1}{2y}$ under the condition $(2xy-1)^2=(5y+2)(y-2)$

Inequality of positive integers

How can I prove that the perimeter is at most 60?

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