- #1
swampwiz
- 571
- 83
AIUI, an algebraic is defined as a number that can be the solution (root) of some integer polynomial, and is any number that can be constructed via any binary arithmetic operation or unary root operation with arguments that are themselves algebraic numbers. I have been able to prove this for almost all cases - with the unproven case being where the number is defined as the addition of a pair of algebraic numbers that happen to have a root operation in each.
Here is an example:
x = a^{1/2} + b^{1/3}
( x - a^{1/2} ) = b^{1/3}
( x - a^{1/2} )^{3} = b
I can't figure out how to continue to de-root a.
Here is an example:
x = a^{1/2} + b^{1/3}
( x - a^{1/2} ) = b^{1/3}
( x - a^{1/2} )^{3} = b
I can't figure out how to continue to de-root a.