Cardano's Method Application

Question

Please forgive me for any mistake in the proposal of this problem

Problem

The first step of Cardano's Method states:-Remove the term containing $x^2$ by taking $y=x-\dfrac{b}{3a}$. However if we are not able to remove the $x^2$ in a equation then how will we solve it.

Any help is welcome. Thanks in advance

Isn't it a contradiction in the problems description? Think about it again! — Fakemistake, Feb 02 '18 at 10:14
Go here $\longrightarrow$ https://www.math.ucdavis.edu/~kkreith/tutorials/sample.lesson/cardano.html — Mr Pie, Feb 02 '18 at 11:54

José Carlos Santos · Accepted Answer · 2018-02-02T10:29:43.153

3

Your question doesn't make sense. If, in $ax^3+bx^2+cx+d$ (with $a\neq0$), $x$ gets replaced by $y-\frac b{3a}$ and then you expand it, you always get a cubic without a monomial with degree $2$, namely$$ay^3+\left(c-\frac{b^2}{3a}\right)y+\frac{2 b^3}{27 a^2}-\frac{c b}{3 a}+d.$$

edited Feb 02 '18 at 10:29

answered Feb 02 '18 at 09:52

José Carlos Santos

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Cardano's Method Application

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