I'm assuming that I can assume that the cube root of 2 is irrational and thus not have to prove it.
f+g*sqrt(h)=2^(1/3) cube both sides
now since all parts of the right hand side are rational then the right hand side is rational thus sqrt(h) must be rational.
If sqrt(h) is rational then so is f+g*sqrt(h) but that would mean that 2^(1/3) is rational which we know to not be true, thus there can not be any rational solutions to the equation
Posted by Daniel
on 2009-07-23 12:34:12