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#### mathmaniac

##### Well-known member

- Mar 4, 2013

- 188

wikipedia said:The depressed quartic can be solved by means of a method discovered by Lodovico Ferrari. The depressed equation may be rewritten (this is easily verified by expanding the square and regrouping all terms in the left-hand side)

wikipedia said:Then, we add a variableyto factor of the left-hand side. This amounts to add some expression to the left-hand side. We add thus the same expression to the right-hand side. After regrouping the coefficients of the power ofuin the right-hand side, this gives the equation

which is equivalent to the original equation, whichever value is given toy.

What does that mean?As the value ofymay be arbitrarily chosen, we will choose it in order to get a perfect square in the right-hand side. This implies that thediscriminant inuof this quadratic equation is zero, that isyis a root of the equation

I also wonder how solving y which is an arbitary number will solve u...which may be rewritten

The value ofymay thus be obtained from the formulas provided in cubic equation.

Whenyis a root of equation (4), the right-hand side of equation (3) the square of

..............................

Can anyone explain the whole process,please???

Then I would be soooo thankful....