Have you observed that x^2 + x + 1 is a factor of an expression involving x^3?i think that is it irrational, so i tried to assume by cintridiction that it is rational.
i comperd the expression to n/m (n and m are integers, m is not zero) and tried to do differnt algebric manipulations to the equation.
i also tried to divide the entire expresion by x^3 and then to assume it is rational but encuterd the same problems.
i tried to find a counter example but culdent find one i can prove is irrational without a calcultor.
i am a little lost at the moment and not sure which direction is practical and would very appreciate sume guidance.
thank you
Use the fact that:so in my first calaules class the professor presented a problem i found hard to solve. will very appreciate the help.
x is irrational
x^3 is rational
prove or disprove
x^2 + x + 1 is rational
Hi prover. That was my first thought because it's the easiest way to disprove that the given quadratic polynomial must represent a Rational number.i tried to find a counter example but [couldn't] find one