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mathmaniac
Active member
- Mar 4, 2013
- 188
I hope its not bad to ask this.
Can anyone explain the whole process,please???
Then I would be soooo thankful....
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 variable y to 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 of u in the right-hand side, this gives the equation![]()
which is equivalent to the original equation, whichever value is given to y.![]()
What does that mean?As the value of y may be arbitrarily chosen, we will choose it in order to get a perfect square in the right-hand side. This implies that thediscriminant in u of this quadratic equation is zero, that is y is 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 of y may thus be obtained from the formulas provided in cubic equation.![]()
When y is 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....