Math Is Fun Forum

Lloyd

Guest

Cubic

Show that the equation

can be reduced to the form

using the substitutions y = x + a and z=by for suitable 'a' and 'b'.

I can get the right answer of a = - 1, b = root3 by making the substitutions separately and examining coefficients. However, if i make the subtitution z = b(x+a), i get:

From which i equate coefficicents to give 4b^3 = 24, which gives b=6^1/3. This then doesn't work when considering the other coefficients. Why doesn't this method work?

Thank you very much.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Cubic

Your identity should be

,

where C is a constant. Can you see why?

This gives

Last edited by Daniel123 (2009-04-07 10:38:23)