Tschirnhausen cubic - expressing in terms of x

Question

Is there a way to express the following function $$y=x\sqrt{x+3}$$ in the form $x$ as a function of $y$?

Thanks

If $\alpha = \frac{1}{4}(4 y + 4 \sqrt{y^2 - 4})^{2 / 3}$, then $x = \alpha + 1 + \frac{1}{\alpha}$. — Travis Willse, Jan 17 '15 at 04:52

score 1 · Accepted Answer · answered Jan 17 '15 at 05:54

1

Hint: Square both sides, and use the cubic formula to extract x as a function of y. Of course, this might introduce some extra solutions. Notice that $x\ge-3$.

answered Jan 17 '15 at 05:54

Lucian

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Tschirnhausen cubic - expressing in terms of x

1 Answers1