MHB Challenge Problem #7: Σ(x/(y^3+2))≥1

Thread starter Olinguito
Start date May 20, 2019
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The discussion revolves around proving the inequality Σ(x/(y^3+2))≥1 for positive real numbers x, y, and z such that xyz=1. Participants are encouraged to explore various mathematical approaches to demonstrate the validity of the inequality. The conversation highlights the importance of manipulating the terms and applying known inequalities to achieve the proof. A hint is provided to guide the participants in their reasoning. Engaging with this problem can deepen understanding of inequalities in mathematical analysis.

May 20, 2019

Olinguito

Let $x,y,z$ be positive real numbers such that $xyz=1$. Prove that
$$\frac x{y^3+2}+\frac y{z^3+2}+\frac z{x^3+2}\ \geqslant\ 1.$$

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Jun 22, 2019

lfdahl

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MHB

A hint ...

is requested (Giggle)

Jun 22, 2019

topsquark

Science Advisor

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lfdahl said:

A hint ...

is requested (Giggle)

Niiiiice. (Clapping)

-Dan

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