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let x ε R. Prove that x is irrational thenI'm confused with a question and wondered if anyone could help explain where I need to go...

let x ε R. Prove that x is irrational then ((5*x^(1/3))-2)/7) is irrational.

I've learnt that this is a proof by contrapositive so set ((5*x^(1/3))-2)/7) to be rational and hence a/b with a,b ε Z and b ≠ 0, and there for x is rational.

But I'm not sure where to go from here. Do I rearrange to find for x? x = ((7a - 10b)/5b)^3

But this is still raational isn't it? Where is the contradiction?

Thanks

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# Contrapositive proof of irrational relations

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