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Let r be a root of x^3 - 2x + 5 = x^3 - x^2 + 9.  Show that none of r, r^2, or r^3 is irrational.

 Apr 14, 2023
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Simplify the expression: \( x^2-2x-4=0\). Use the quadratic formula to get 

\(\frac{2 \pm \sqrt{(-2)^2-4\cdot1\cdot(-4)}}{2}\)

\(\frac{2 \pm \sqrt{4-(-16)}}{2}\)

\(\frac{2 \pm \sqrt{20}}{2}\)

\(1 \pm \sqrt{5} = r\)

So r is irrational, so this cannot be done.

 May 4, 2023

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