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The polynomial equation x^3 + bx + c = 0 where b and c are rational numbers, has 1 + sqrt(2) as a root. It also has an integer root. What is it?

 Jun 5, 2022
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(x-(1+sqrt2))(x-(1-sqr2)(x+a)

 

\((x-(1+\sqrt2))(x-(1-\sqrt2)(x+a)=0\\ (x-1-\sqrt2)(x-1+\sqrt2)(x+a)=0\\ ((x-1)^2-2))(x+a)=0\\ (x^2-2x-1)(x+a)=0\\ \)

 

 

Yoou can check and finish it.

 Jun 6, 2022

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