**Ferrari’s solution of the Biquadratic. **

Writing the equation …**Equation A**

we assume that …**Equation B**

Expanding and equating coefficients, we have

and and ….**Equation C**

Eliminating m, n,

which reduces to

…**Equation D**

The second term can be removed by the substitution …**Equation E**

and the equation D becomes …**Equation F, which is the “reducing cubic”. **

Equations C become

**Call the above three equations as G.**

Thus, if is a root of F and

and , the equation

can be put in the form

,

and its roots are the roots of the quadratics

.

**It should be noted that the three roots of F correspond to the three ways of expressing u as the product of two quadratic factors.**

**Homework: **Solve the equation .

Hope you enjoyed it…

More later,

Nalin Pithwa

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