Sorry, do you mean, solve ?
EDIT:// I checked your work and there seems nothing wrong with your method. It is quite slick to think of
You could always use polynomial expansion, foiling out if you like, but that wouldn't seem to be worth the effort
You are dead on with your explanation (that -2 is the other answer). I believe this is the step where the oversight was:
When dealing with an equation involving powers, it is insufficient to take simply the principle root. For an equation of real numbers involving an even power, there are always two roots of positive numbers (the principal root and the negative of the principal root). So implies that or . For odd powers, there is only one root of a positive number. So means the only solution is
If you are dealing with equations over the complex numbers, things are different. By the fundamental theorem of algebra, there roots for a polynomial of degree . So has solutions for . So can picture the solutions as vertices of a polygon in the complex plane (as seen here), with one vertex at the principal root. For even powers you have the symmetry of flipping around the vertical axis which is not present in odd powers.
Double posting is forbidden
http://www.mathhelpforum.com/math-he...-decrease.html
I'm sorry for double posting
however, on this post, i asked a question that dealt with the algebra part of the problem, it was an algebra concept that I couldn't understand, on the other post, it was a calculus concept.
Should I put it both in one thread next time?