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

170

Views

Inequality $\dfrac{1}{\sqrt{1+2x}} + \dfrac{1}{\sqrt{1+2y}} + \dfrac{1}{\sqrt{1+2z}} \leq \sqrt{3}$.

Published on 25 Jan 2021 - 12:41

71

Views

Proving each subsequent term equal to one another in an equation

Published on 25 Jan 2021 - 14:05

134

Views

Minimum of a function by inequality

Published on 28 Jan 2021 - 1:24

81

Views

Solving AM-GM without expanding

Published on 28 Jan 2021 - 13:59

728

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Sum of square roots inequality

Published on 29 Jan 2021 - 20:55

175

Views

Reciprocal inequality

Published on 29 Jan 2021 - 21:53

81

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Prove $\frac{x}{y^3+2xyz} + \frac{y}{z^3+2xyz} + \frac{z}{x^3+2xyz} \gt \frac{15}{2}$

Published on 02 Feb 2021 - 7:13

1k

Views

Min $P=\frac{x^5y}{x^2+1} +\frac{y^5z}{y^2+1} +\frac{z^5x}{z^2+1}$

Published on 02 Feb 2021 - 8:22

81

Views

Prove that $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \geq \sqrt{a}+\sqrt{b}+\sqrt{c}$

Published on 03 Feb 2021 - 5:12

279

Views

maximum and minimum value of $(a+b)(b+c)(c+d)(d+e)(e+a).$

Published on 04 Feb 2021 - 2:38

95

Views

Question on finding maximum of AM GM inequality

Published on 05 Feb 2021 - 3:52

337

Views

Existence of a factorisation proof of the AM-GM inequality

Published on 31 Mar 2026 - 23:09

110

Views

If $x+y+z+a+b+c=1$, $xyz+abc=1/36$, what is the max value of $abz+bcx+cay$?

Published on 13 Feb 2021 - 14:55

128

Views

Prove that $\frac{x^2+y^2}{z}+\frac{y^2+z^2}{x}+\frac{z^2+x^2}{y}\geq 2(x+y+z)$

Published on 13 Feb 2021 - 16:03

121

Views

If $x+2y=8$, find the minumum of $x+y+\frac{3}{x}+\frac{9}{2y}$ (x, y ∈ R+)

Published on 14 Feb 2021 - 1:43

List Question

Inequality $\dfrac{1}{\sqrt{1+2x}} + \dfrac{1}{\sqrt{1+2y}} + \dfrac{1}{\sqrt{1+2z}} \leq \sqrt{3}$.

Proving each subsequent term equal to one another in an equation

Minimum of a function by inequality

Solving AM-GM without expanding

Sum of square roots inequality

Reciprocal inequality

Prove $\frac{x}{y^3+2xyz} + \frac{y}{z^3+2xyz} + \frac{z}{x^3+2xyz} \gt \frac{15}{2}$

Min $P=\frac{x^5y}{x^2+1} +\frac{y^5z}{y^2+1} +\frac{z^5x}{z^2+1}$

Prove that $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \geq \sqrt{a}+\sqrt{b}+\sqrt{c}$

maximum and minimum value of $(a+b)(b+c)(c+d)(d+e)(e+a).$

Question on finding maximum of AM GM inequality

Existence of a factorisation proof of the AM-GM inequality

If $x+y+z+a+b+c=1$, $xyz+abc=1/36$, what is the max value of $abz+bcx+cay$?

Prove that $\frac{x^2+y^2}{z}+\frac{y^2+z^2}{x}+\frac{z^2+x^2}{y}\geq 2(x+y+z)$

If $x+2y=8$, find the minumum of $x+y+\frac{3}{x}+\frac{9}{2y}$ (x, y ∈ R+)

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