Monday, 8 February 2016

Prove sqrt1+sqrt[3]2 is irrational using the theorem about rational roots of a polynomial




I'm having trouble with this specific problem at the moment. The theorem states that if n/m is a rational root of a polynomial with integer coefficients, the leading coefficient is divisible by m and the free coefficient is divisible by n.



Using this theorem, I'm supposed to prove that 1+32 is irrational.
I don't have any idea where to start on this one.



Any help or hints are appreciated.


Answer



You want to use the rational root theorem.




Hint: Let x=1+32, then, x2=1+32, so (x21)=32. Hence, (x21)3=2.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...