1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding Polynomials from their Zeros

  1. Jun 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Prove that x = 2^(1/2)+2^(1/3) is irrational.

    2. Relevant equations

    3. The attempt at a solution

    The hint to the exercise says that I should first show that x satisfies an equation of the form x^6+a_1*X^5+...+a_0 = 0, where the coefficients are integers.

    I am having trouble showing that x satisfies such an equation.

    I tried multiplying (x-2^(1/2)-2^(1/3))(x+2^(1/2)-2^(1/3)) but was not successful in getting integer coefficients.
  2. jcsd
  3. Jun 11, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Try putting some more factors in.

    Or just start from


    and manipulate it to find an expression x satsifies. (eg, if x=sqrt(2), then squaring both sides yields x^2=2, so x satisfies x^2-2=0. n.b. don't square both sides of what you started wit -try something more sophisticated than that).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook