Another form of cubic folium equation

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SUMMARY

The discussion focuses on transforming the cubic folium equation, specifically the equation x³ + y³ = 3axy, into the form x + y = 3a / (x/y + y/x - 1). User bluemoon2188 seeks assistance in this mathematical transformation, and henry_m provides a solution by factoring the original equation. The transformation utilizes the identity (x + y)(x² - xy + y²) to facilitate the conversion.

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bluemoon2188
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Hello,

I am looking for a way to express the equation of folium

x3 + y3 = 3axy

into

x + y =\frac{3a}{\frac{x}{y}+\frac{y}{x}-1}

thanks

bluemoon2188
 
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<br /> x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)\left(\frac{x}{y}+\frac{y}{x}-1\right)xy<br />
 
Last edited:
Oh coo.l. Thanks henry_m.

bluemoon2188
 

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