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Prove that following equations have no rational solutions. a) x^3 + x^2 = 1 b) x^3...

Prove that following equations have no rational solutions.

a) x^3 + x^2 = 1

b) x^3 + x + 1 = 0

d) x^5 + x^4 + x^3 + x^2 + 1 = 0

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