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thenthanable
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Prove that if x satisfies
My main question is that I don't quite understand what the question is trying to ask me prove. I'm fairly new with this so pardon me if this question is really basic. Am I suppose to prove that x is irrational or an integer? The 'unless' in the question really throws me off.
Nonetheless, I came up with a few ideas because I must say I really suck at proofs so I always begin by writing down things I notice about the equations given.
I wrote that the above equation is the binomial expansion of (x+(ao)1/n)n = 0, and if ao gives an integer solution, then x= -(ao)1/n so x is an integer? But then again, I'm not very sure what the question really wants. :S This question is madly confusing to me! :(
'xn +an-1xn-1+ ... a0=0'
for some integers an-1,..., a0, then x is irrational unless x is an integer.My main question is that I don't quite understand what the question is trying to ask me prove. I'm fairly new with this so pardon me if this question is really basic. Am I suppose to prove that x is irrational or an integer? The 'unless' in the question really throws me off.
Nonetheless, I came up with a few ideas because I must say I really suck at proofs so I always begin by writing down things I notice about the equations given.
I wrote that the above equation is the binomial expansion of (x+(ao)1/n)n = 0, and if ao gives an integer solution, then x= -(ao)1/n so x is an integer? But then again, I'm not very sure what the question really wants. :S This question is madly confusing to me! :(