Polynomial with root $α = \sqrt{2}+\sqrt{5}$ and using it to simplify $α^6$

Hint

$a^2=(\sqrt{2}+\sqrt{5})^2=2+5+2\sqrt{10}=7+2\sqrt{10}\Rightarrow a^2-7=2\sqrt{10} \Rightarrow (a^2-7)^2=40$

Edit

$(a^2-7)^2=40 \Rightarrow a^4-14a^2+49=40 \Rightarrow a^4-14a^2+9=0$

Tags:

Polynomials

Abstract Algebra

Roots

Field Theory

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